ya vat 


Ln * 
bes ane Pej abs 
Me ntti fue 


Heit iy Petey 
sia We Bet» 

i fobs Polk 
ele or retard 
ver Sats Ue bone 
§ obbdnlhy bah hep h ty 


ak 


ts i 
oad 
bath Pott 
eit 


ay 
ftir 
Abas itt 
by ibe 
seth hae Pdr 


of esa 
ile 


Nie 


{yt she a 


7 
heels 

aa 
ie th aa 
hi 


Ba Meee 


Wi 

a pepay 

ho 
i 


tie if 
henry yy neatt ta heasae 


tie beget 
*} ut Rt ise 14a4? 
#2 


a ‘4 anh 
4 

it it fon iPe 
sat 


reek 
SRLS ioe 


sae behaeua’ 


th eae siti stares Butea oo a ; He fay saved 
Vee Neate ed 
Mia} i) iY W 4bp bhevaie Uh! Ghat olde ua 


HOSP yen a 


ita thnste ite 


a te ah * aah : by om 


= 
= 


Se Sten 


tiemNe ait 
its 
1 hia tis 
re jan) Hy ti 
Des tae 


) Ne iteedat ob 
nie ade Bola aes rine 
iuey vai i teh hd, soit a Hf i ae 


ait cA 


i 


: 
‘ ES 
va a ath 
esd 
wi A 8 
Tobe f ? 
a a 


fay - 


Sy 


saat 


ate 


Peas ne 
tt ste Hehe 


te 
eighth 


ae Hate i 


% aM 
ne re hy 


bead) ee 


A. 
1a f 
A} ce Rises arid 


pen 
asada, 
reheat etn 


A ‘mate 
anita eile ee 
Va eho pede + 
Ai he K i, ate be 
aati he t as 
Wahi ee ; rn fy 
ain aah ihe ee 


fe 


hear 
Seri Ih 
ea i a 


ae 


vee His 
ae 
a 
Si 18 i r 
patent eitae 
Peay oo 
+ Maes 


3 


ee 


pares OF Be: *b 
pease 
ai ieidiee: bitte 
” vit Mt a foil tia i 
DROP vos satin 
yi \ 
werseyd us 
> Harts 


" acyasit ereres 
aiitints 


citi 
eins ata 


Tat ORS 
a) dif ’ 
ihe inert Heat i 


Gs pea Aga py 
Oth 
HER eis aie 


ted 


Wieiiay? 
et ay Fe sted 


: v7 
| Pele f ry Fs tae ‘ i ti 
Lint othe bth) nee ru ty Hite ah H Ft bai 

ms it ; ata ite an 
sity a peed 


beds aide te Ug 
pigs oleie 


haeane 
angie? i 
ieee ‘at jel 
a4 

a 


ba n st att vi ee 
el nie Pee a onnen manta ane 
ee 
Ai if , bh Ot . 
He p ie earth re iiNhutt 
tk f 


a 












jf ai } a 
V/ L) ! , Wy 


5 / 
atl Vv PSYCHOLOGICAL REVIEW PUBLICATIONS bee eke 1 


Psychological Monographs 


EDITED BY 


SHEPHERD I. FRANZ, Univ. or Cauir., So. Br. 
HOWARD C. WARREN, Princeton University (Review) 
JOHN B. WATSON, New York (J. of Exp. Psych.) 
MADISON BENTLEY, Unrversirty or Ittinots (Index) and 
S. W. FERNBERGER, University or PENNSYLVANIA (Bulletin) 


The Influence of the Factor of 
Intelligence on the Form of 
the Learning Curve 


By 
GILES MURREL RUCH 
UNIVERSITY OF IOWA 


PUBLISHED FOR 
Tue AMERICAN PsycCHOLOGICAL ASSOCIATION 


By THE PSYCHOLOGICAL REVIEW COMPANY 
PRINCETON, N. J. 
anp ALBANY, N. Y. 


Acents: G. E. STECHERT & CO., Lonpon (2 Star Yard, Carey St., W. C.) 
Lerpzic (Hospital St., 10); Paris (76, rue de Rennes) 


Digitized by the Internet Archive — 
in 2022 with funding from ae 
Princeton Theological Seminary Library ~ 


ita 
ja tne 
oe 


https://archive.org/details/influenceoffacto0Oruch ih 








ACKNOWLEDGMENTS 


In the course of this investigation the writer has necessarily 
become deeply indebted to a number of persons. It is a great 
pleasure to make specific acknowledgment of the invaluable assist- 
ance given by Professors Lewis M. Terman and Truman L. 
Kelley of Stanford University. The completion of the study 
was made possible through the granting of a University Fellow- 
ship for.the year 1920-21 and a Research Fellowship for the year 
1921-22. Acknowledgment is due the Committee on Graduate 
Study and to Professor Terman for these awards. Professor 
William T. Root, Jr., now of the University of Pittsburgh, gave 
much appreciated aid in the formulation of the experimental 
procedure. Through the cooperation of Dr. Virgil E. Dickson, 
Mr. William M. Greenwell, Mr. Charles E. Keyes, and Mr. John 
R. Sutton, a large number of children in the city schools of 
Oakland, California, were made available for subjects in the 
-experiments. Mr. Cecil R. Brolyer, of Stanford University, 
gave valuable assistance in supervising the compilation and treat- 
ment of the experimental results. Dr. Arthur S. Otis, of the 
World: Book Company, was kind enough to read and criticize 
certain parts of the statistical treatment. 


ta EO PASE 
Fea ae fi ye, j at 
Rei sth | fai Ds 


eae F 
eA 7 bp karan 


Pt eM LAR 


At Oe 


Wve ls 
ave) fn 


1 | ae 
A, 7 co A ‘ 
4 a ’ 

F nyo? 





CONTENTS 


CHAP. PAGE 

I. INTRODUCTION AND STATEMENT OF THE PROBLEM... 1 

Piel oe, LITERATURE OF THE PROBLEM.» clas ov ve tees 4 
III. DeEscriPpTION OF THE METHODS OF THE INVESTIGA- 

cae feet ee Bech Fs pee U0 Tn eaWn Sty rd oes SRA Ci Se ee 14 

Ve We UX PERIMENT AL IG ESULTS a oU sla ely Ole elaine dds 26 
V. STATISTICAL TREATMENT AND INTERPRETATION OF 

he EW yh Re ASU ate a RR ald Ie a Ne A ale 27 

hee UMMARY. AND GON CLUSIONS issn cae ons wes selene a wie 57 

AQ) GORSPIN@ €08s OOkR FARR RD URC at UES Acne aa TOE nme Oi ea 59 


y 5 j 
wd 4 vi > i Ne te ‘4 Ti ry pan hy 
Nag eu VR b 


4 ; july Fe 
‘Ki 


as) etal | easton a 6} 
gama net te be Wd 


iw ; : : 
ee ee ee 





GCHAPLR Rak 
INTRODUCTION AND STATEMENT OF THE PROBLEM 


The present investigation is primarily an attempt to bring 
under control and measurement certain factors which are opera- 
tive in producing individual differences during the practice of 
mental functions. Most experimental studies which have taken 
cognizance of such individual variations at all have done so in 
one or both of two principal ways. The first of these problems is 
that of the quantitative measurement of the amounts of indi- 
vidual variability in the ability to profit by training, and the 
second is the question whether practice increases or decreases 
these differences in the performance of various subjects. 

With respect to the first of these two issues it is now common 
knowledge that relatively great differences in such capacities do 
exist and the present interest in this question has narrowed down 
to the statistical expression of these differences in terms of valid 
objective units. The second question, on the contrary, has not 
yielded an unambiguous answer and no generalizations of great 
significance have been forthcoming. Many psychologists have 
held firmly that practice decreases or levels down those differ- 
ences, innate or learned, which are present in the initial perform- 
ances in the formation of new sets of nerve connections. To-day, 
the opinion tends to the position that these differences are increased 
by further exercise of the functions involved. 

The experimentation which is reported here was planned to 
attack this problem of the increase or decrease of individual 
differences under practice in such a way as to control and measure 
the influence of two factors which are believed to be prominently 
involved in the behavior and fate of these differences. Specifi- 
cally stated, the problem is to study: (1) the influence of the 
type of mental function which is involved in the learning, and 
(2) the influence of the factor of general intelligence or the 
general mental level of the subjects used. 


Z GILES MURREL RUCH 


In the main, learning studies have involved very small numbers 
of subjects who were usually adults. For this reason, probably, 
the question of the possible influence of innate or acquired dif- 
ferences has not ordinarily been raised. There are surprisingly 
few studies of the learning of children and almost no investiga- 
tions where the subjects have been carefully classified and meas- 
ured with reference to the general mental ability of the learners. 
Conceivably this might prove to be a factor of great significance. 
As a matter of fact teachers have seemed more aware of the 
importance of intelligence in learning than have the laboratory 
investigators. 

In the second place there is probably an unwarranted tendency 
to generalize too largely about the learning curve as if one par- — 
ticular form of a curve obtained for all types of mental functions. 
We have, indeed, suggested several general categories of learning 
types, such as “sensorimotor,” “ perceptual,” “ ideational,” etc., 
without raising the question of the possibility of these being 
found to possess widely divergent characteristics with respect to 
the form of their learning curves. It is well within the bounds 
of reason to expect that the intellectual superiority of a gifted 
individual might not give him as great an advantage over a less 
gifted individual in his performance in such a relatively simple 
situation as cancellation of a’s or sorting cards as in the mental 
multiplication of three-place numbers or in a completion exercise. 
If this be true, it is of little gain to generalize about the course of 
individual differences under practice without specific reference to 
the kind of learning involved. 

To measure the influence of these two factors, viz., general 
mental ability and the type of mental function undergoing prac- 
tice, the selection of the subjects in the present experiment had 
to be carried out in a definite manner. The chronological age 
range was kept as small as was practicable under the actual con- 
ditions of securing the necessary subjects. At the same time the 
mental age range was made as great as conveniently possible in 
order that the extremes of mental ability might be well represented 


‘ 


in numbers. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 3 


The selection of suitable tests offered considerable difficulty. 
In order to vary the type of mental processes to be studied, in 
accordance with the previously discussed requirements, and not 
make the experimental work prohibitive in amount, it was desir- 
able to select a small number of tests which would, in a sense, 
sample the whole range of possibilities from ‘‘ motor” learning 
on the one hand to the so-called “ higher thought processes” on 
the other. Tests of sensorimotor capacities are fairly numerous, 
and one, card sorting, which has been used by many investigators 
(Bergstrom, Burt, Coover, Brown, et al.) was finally selected as 
representative of its type. As a second test which would involve 
comparatively little of the motor element and which would call 
for use of sensational and perceptual processes, a modification of 
the Healy Civil War Code was adopted. The selection of a third 
test needed for the study of learning on a highly intellectual level 
proved to be very difficult. The possibilities included such tests 
as the analogies, completion exercises, mental multiplication or 
addition, and a few others. Unfortunately none of these exist in 
several comparable forms and it is difficult to measure the effh- 
ciency of the learning of such materials from day to day. The 
final choice was that of an abstract mathematical relations test 
which will be described in greater detail in a later section. No 
claim is made that the location of these three tests with respect 
to their psychological characteristics and demands is based upon 
any more exact knowledge than a considerable amount of tra- 
ditional agreement in the terminology of the literature of learning. 
The real intention, as has already been stated, was merely that of 
sampling a fairly wide range of mental capacities. 


CHAP EER tit 
Tue LITERATURE OF THE PROBLEM 


The attempt to summarize even the important experimental 
work that has been done on the general problem of individual 
differences in learning capacities would not be warranted by the 
pertinence of much of this literature to present needs. Never- 
theless reference must be made to a number of the older studies 
which have only indirect bearing in order to give the proper 
historical orientation for certain controversies which must be 
taken up later. Recently there has grown up something of a 
literature on the relation of intelligence to learning. This 
demands somewhat more careful consideration. 

For these reasons, the selection of the papers to be reviewed 
will be restricted to three groups, viz.: (1) Representative older 
studies of the increase or decrease of individual differences dur- 
ing practice, of the relations existing between initial and final 
efficiency in learning, and of the course of the behavior of inter- 
correlations between mental functions under practice; (2) 


studies of card sorting, substitution, and reasoning abilities in 


tests similar to those of the present study; and (3) studies of 
the learning of subjects classified according to general mental 
ability, or where the learning has been measured with statistical 
reference to general intelligence. 

Obviously only the investigations of the third type are direct 
in their significance for present purposes. References to the 
literature will be made in accordance with the foregoing classi- 
fication. 


I. Investigations of the Effects of Practice on Individual Differ- 
erences: 

Binet (1899:4) concluded that for several forms of cancella- 

tion tests the differences between bright and dull pupils present 

at the outset tended to disappear with continued practice. He 


eatery 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 5 


says: ‘La différenciation est nette surtout dés la premiére 
épreuve; elle diminue et peut meme s’effacer aux épreuves 
subséquentes ” (p. 395). 

This conclusion was attacked by Spearman and Krtger (1907: 
39) on the basis of their results obtained by refiguring data gath- 
ered by Oehrn in 1899 on continued adding. They replied to 
Binet as follows: ‘“ Binet hat, wie schon gesagt, die Meinung 
ausgesprochen, dass derartige Korrelationen nur bei ungewohnten 
Versuchsbedingungen deutlich hervortreten; mit zunehmender 
Uebung sollen sie rasch kleiner werden, manchmal sogar ver- 
schwinden. Der eine von uns wurde jedoch zu dem entgegenge- 
setzten Schlusse gefuhrt, dass bei genauer Untersuchtsmethode 
die Uebung . . . die Korrelationen sogar vergrossert” 
(p. 96). 

Burt (1909:7) studied the same problem but discussion of his 
results, which are not very conclusive, will be reserved until a 
later section. 

From 1908 on, Thorndike and his students have carried out a 
series of investigations of individual differences in mental capaci- 
ties. Thorndike’s own paper (1908:46) presented the general 
tenor of all of the conclusions reached in this group of studies 
when he says, with reference to multiplication of three-place 
numbers, “. . . the larger individual differences increase with 
equal training, showing a positive correlation of high initial 
ability with ability to profit by training” (p. 384). During the 
five years from 1911 to 1916, Donovan and Thorndike (1913 :15), 
Hahn and Thorndike (1914:18), Starch (1911:41), Kirby 
(1913 :24), and Thorndike himself in several studies (1910 :49, 
1914:47, 1915:48), brought forward additional evidence that 
practice in mental operations in arithmetic resulted in increasing 
the differences present at the outset. In one of these, (1914 :47) 
after reviewing the work of Galton, Cattell, Rice, and his own 
study of men entering learned professions, he summarizes by 
saying: ‘‘ The facts are rather startling. Equalizing practice 
seems to increase differences. The superior man seems to have 
got his present superiority by his own nature rather than by 


6 GILES MURREL RUCH 


superior advantages of the past, since, during a period of equal 
advantages for all, he increases his lead” (p. 305). 

Wells (1912:52) reported that the learning curves of ten dif- 
ferent subjects rarely crossed, and that “. . . a superior per- 
formance at the beginning of special practice is not necessarily or 
even probably attained at the sacrifice of prospects for future 
improvement” (p. 88). 

Hollingworth,(1913:19) from the use of adding, toler nam- 
ing, opposites, discrimination reaction to colors, coordination 
(3-hole test), and tapping, concluded that the average intercor- 
relations of the six tests increased from trial to trial, at least up 
to certain stages. This point was about the twenty-fifth trial for 
discrimination and the eightieth trial for adding. The average 
intercorrelations were .065, .280, .320, .390, and .490 for the 
medians of trial 1, trials 1-5, 20-25, 75-80, and 200-205, respec- 
tively. Hollingworth warns against the use of the initial trials 
as measures of ability and favors trials nearer the limit of effi- 
ciency. Cancellation showed a correlation of .665 between initial 
and final efficiency but opposites yielded but —.088 between the 
preliminary and 130th trials. The coefficient for adding was 
.154 under the same conditions. The number of subjects was 


but thirteen and all were adults. Hollingworth himself has 


pointed out that cognizance must be taken of the possible effects 
of changes in the test functions due to habituation during the 
long practice periods in interpreting his results. 

Whitely (1911 :54) reported the results of nine adults of vary- 
ing levels of ability in tests of discrimination of weights, cancel- 
lation of A’s, sorting, and the pencil maze. Correlations of about 
.50 between starting ability and gross gain were computed. These 
results are not in accord with the findings of others and even 
certain of Whitely’s other findings and have been objected to by 
Thorndike and others. 

Chapman (1914:9) found high correlations between initiai’and 
final performances in color naming, cancellation, opposites, and 
multiplication, the coefficients ranging from .59 to .96 in a group 
of twenty-two male college students. 


ae. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 7 


Jones (1917 :23) has held that the results of Wells, Chapman, 
and Hollingworth are opposed to Thorndike’s position. He 
refers specifically (p. 20) to the fact that the Wells subjects who 
gained most in addition gained least in cancellation. This raises 
an issue which will be returned to after our new data have been 
presented since it is typical of one of the controversial interpreta- 
tions of experimental results with which the literature of learning 
abounds. 

Strickland, (1918 :43) using the Woodworth-Wells color-nam- 
ing test, adding, tapping, multiplying, and word building, 
found that “ where practice improves performances correlations 
increase’. (p. 399). 

A belief in a “general capacity for learning” has been 
expressed by Pyle (1919:35). Such a capacity is dependent 
upon the characteristics of the nervous system itself and would 
operate to cause intercorrelations between separate tests to 
approach unity if the extraneous factors could be eliminated. 

Many apparent inconsistencies are to be noted in the foregoing 
account, and the conclusions are by no means unambiguous. 
The variety of, mental processes measured, the probable great 
differences of mental ability among the subjects used, and the 
variations in the points of view and statistical methods have all 
contributed to produce these conflicting interpretations. On the 
whole there seems to be a preponderance of evidence in favor of 
the view that practice tends to increase those differences present 
in human beings at the beginning of learning situations, at least 
for such complex mental functions as the mental solution of 
arithmetical problems and reasoning abilities in general. For 
tasks like cancellation and sensory discrimination, the evidence is 
uncertain and the formulation of definite conclusions is better 
omitted until our new data have been presented. 


II. Investigations of Card Sorting, Substitution, and Reasoning 
Abilities: 

Card sorting as a test of mental ability has been used by many 

investigators for one purpose or another, e.g., by Bergstrom 


8 GILES MURREL RUCH 


(1894 :3), Coover and Angell (1907 :11), Culler (1912 :12), Cal- 
fee (1913:8), Kline and Owens (1913:25), Brown (1914:6), 
Myers (1918:30), Pyle (1919:35), et al. Bergstrom, Culler, 
Kline and Owens, and Brown were chiefly interested in studying 
the effects of interference in habit formation. Coover and. 
Angell emphasized the great individual differences in the imagery 
and other mental processes of the several subjects and in the same 
subject at different stages in the learning process. However, 
none of these studies involved card-sorting techniques which 
resembled at all closely the one used in the present study. 

Calfee has reported correlations between the sorting of cards 
face up and the sorting the same face down (dealing) ranging 
from .45 to .71. Of card sorting, card dealing, alphabet sorting, 
and mirror writing, the first mentioned gave the highest correla- 
tion with school grades of children. 

Myers has stated that ‘“ practice does not make the individuals 
more or less alike” (p. 325). He refers to card sorting. 

Substitution tests have been used in a variety of forms by 
many workers, e.g., Gray (1918:17), Baldwin (1913:2), Starch 
(1912 :42), Lough (1912:27), Munn (1909:29), Pyle (1913: 
34), Squire (1912 :40), Woodworth and Wells (1911 :57), Wool- 
ley and Fischer (1914:58), Dearborn and Brewer (1918:14), | 
and many others. The last mentioned only used the Healy Civil 
War Code. Their methods differed so greatly from those of 
this investigation that comparisons cannot be made even in this 
case. Dearborn and Brewer’s work, although chiefly intended 
as a university class demonstration, brought forth certain results 
of interest, viz., “ the students tend to hold the same 
relative rank in the first trials as in the last trials of the practice ” 
(p. 81). Whipple (1915:53) gives a good summary of the 
literature and norms on substitution tests (pp. 499-515). Weid- 
ensall (1916:51) used the Woolley and Fischer substitution test 
with delinquent women and found a correlation of .48 with 
estimated intelligence after several practices. 

Bonser (1910:5), Ruger (1910:37), Peterson (1920 :33), and 
many others, have worked with tests of reasoning capacities. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 9 


None of these resembles at all closely the “Abstract Relations ” 
test of our experiments and hence need not be commented on at 
length. Bonser presents evidence that the abilities of naming 
opposites, controlled association, selective judgments, and even 
literary interpretation are closely related in their psychological 
nature. 

Ruger has carried out an introspective analysis of the puzzle- 
solving consciousness with trained adult observers. 


III. Studies of Learning in Relation to General Intelligence. 


Dating from the time of Binet there have been perhaps some- 
what more than a score of studies which directly or indirectly 
have involved a certain amount of consideration of the influence 
of intelligence as a factor in learning. Binet has already been 
quoted as believing that dull subjects in certain tests (cancella- 
tion) reach a final efficiency equal to that of bright ones. 

Kuhlmann (1904:26) found that the learning curves of three 
Mongolian imbeciles and six feebleminded in target throwing and 
tapping maintained their relative ranks rather closely. 

Terman’s study (1906:45) of seven “bright” and seven 
“stupid”’ boys presents a detailed account of the differences in 
the capacities of these boys in the higher mental processes, e.g., in 
puzzle solving, tests of invention, the ball and field test, mathe- 
matical problems, language usage, mutilated texts, fables, mem- 
ory, chess playing, et al. The “bright” group proved much 
superior to the “ stupid ”’ in all the mental tests used, there being 
the least difference in the tests of invention. The subjects 
maintained their relative ranks with great uniformity. 

Burt (1909:7), with a battery of twelve tests (sensory dis- 
crimination, tapping, card sorting, mirror writing, spot-pattern, 
dotting, etc.), tested English school children in considerable num- 
bers and found that eleven of the twelve tests gave a lower cor- 
relation with imputed intelligence on the second trial than in the 
first. The differences are small, however, and probably not very 
significant. 

Abelson (1911:1) failed to verify Burt’s results but found on 


10 GILES MURREL RUCH 


the contrary definite tendencies for correlations to rise with repe- 
tition of the tests. Abelson observes with reference to Burt’s 
tests that: ‘‘ His easier ones may well have been tests of intel- 
lectual power to normal children when first tried, but tending to 


become mechanical in repetition; in that case the more defective | 


children would no longer be at such a disadvantage. Mentally 
deficient children, on the other hand, would not readily master a 
performance sufficiently to make it mechanical but would have to 
continue to exert their full powers” (p. 305). 

Simpson (1912 :39) compared a group of “ good”’ and a group 
of “ poor” adults with a wide range of tests from motor control 
to “ selective thinking.” His main interest was that of a critique 
of the Spearman theory of a “ general factor” and his results 
have little bearing here. Simpson does comment on the data 
published by Oehrn and refigured by Spearman and Kruger to 
the effect ‘that increase or decrease would depend upon the 


9 


kind of a test and the stage of the subjects in the learning | 


DOCS a ea DAO, 

Colvin (1915 :10), Woodrow (1916-7 :55), Ordahl and Ordahl 
(1915:31), and Murdoch (1918:28) have studied the learning 
of subjects of the same mental ages but of differing chronological 
ages. Woodrow used the problem of sorting gun wads on which 
had been pasted various geometrical designs. The following 
have been selected from his results (Table III, p. 936 and 
elsewhere) : 


Aver. Aver. Aver. Aver. per 
Group Aver. Initial Final Improve- Cent of 
N. M. A. Trials Trials ment Improv. 
Feebleminded 20 8-10 121 175 55 49 
Normal 9-1 122 17640 55 46 


All of these studies seem to show that the learning curves of 
subjects of equal mental ages are strikingly similar regardless of 
the great difference in actual ages, except that of Murdoch, who 
found that normal children improved more in educational tests 
over a period of a year than did feebleminded children of the 
same mental age. But, as L. S. Hollingworth (1920:21, p. 178) 
has pointed out, Murdoch did not take into account the fact that 


ae 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 1 


“ the children do not remain of equal mental age’ over the period 
of the experiment, due to the more rapid mental growth of the 
normal group. Woodrow’s experiments do not involve this time 
error since all of the experimental work was done within a space 
of about two weeks. 

There is almost general agreement that, even where the 
improvement is equal, the learning curves of the feebleminded 
show greater daily fluctuations and irregularities than do those 
of normal children of the same mental ages. 

Gould and Perrin (1916:16), using a group of adults and a 
similar group of children as representing two groups of varying 
intelligence, compared their curves in maze learning. They con- 
cluded that intelligence is manifested chiefly in the initial stages 
of the learning and that the controlling factors in the later parts 
of the curves are fatigue and motor control. But they also find 
that the intelligent learners (the adults) make poorer records on 
the first two trials than do the less intelligent learners (children) 
and show a steeper initial rise with greater freedom from steeples. 
One is tempted to raise the issue here, in view of the results, 
whether the difference between children and adults in such a 
function is a matter of intelligence alone and whether such other 
factors as may be involved hold true explanation of these results. 
Perrin (1919:32), comparing the learning of adults in the analo- 
gies and mirror reading tests, found no correlation between the 
rankings of the subjects in the two tests, the superior subjects 
being at their best the farther they were away from the physio- 
logical limit of improvement in mirror reading, and the nearer 
they were to their limit in the analogies test. These relations 
were reversed in the inferior group. One of Perrin’s conclusions 
is of interest here: “In one respect, the demonstrated lack of 
relationship is significant. It furnishes justification for the con- 
clusion that the similarity between the tests as regards slope, the 
greater improvement of the inferior subjects, and the reliability 
of the initial scores as indices of future accomplishment, is due to 
the nature of the tests themselves, rather than to the personnel of 


12 GILES MURREL RUCH 


the practicing group” (pp. 59-60, italics mine). The correlations 
between initial scores and subsequent improvement were: 


Mirror reading. 25.2026. . 85 to .94 
AWalogies.; we geese cac ee COTO 


Perrin sums up his opinions on the relation of intelligence to 
learning in the further statement that: “ intelligence thus 
becomes defined in terms of immediate, consistent, and uniform 
adjustment, not in adjustment considered as a capacity for 
improvement by leaps and bounds” (p. 51). 

Wallin (1916:50) practiced large numbers of children on form 
boards. The average group improved most, the dullest next, and 
brightest group somewhat less than the dullest. 

Strong (1917:44) says: “The slope of the learning curves 


of school children based on simple arithmetical combinations. 


apparently correlates to a very considerable extent with the gen- 
eral intelligence of the children” (p. 153). Strong does not, 
however, present objective data in support of this conclusion. 

Myers (1918:30) has already been reported as finding no cor- 
relation between the intelligence of normal school children and 
their abilities in card sorting. | 


Dallenbach (1919:13) divided a group of feebleminded chil-- 


‘ D8) 166 


dren into “ superior, medium,” and “inferior” groups for 
study with visual apprehension of numerals, letters, words, and 
geometrical designs and figures. He used also a group of normal 
children for purposes of comparison. Mental age correlated with 
standing in visual apprehension as follows: 


Before practice........ 0.70 = .056 
After practice)... ,4:.% 0.63 = .094 


He states that: “ Individual differences are marked, but they 
are closely correlated with the mental age” (p. 82). 

Johnson (1919 :22) studied three groups of five adults each 
in a target throwing test. The chronological ages of the subjects 
ranged from about eighteen to twenty-eight years, and the mental 
ages from about eight to seventeen years. The groups were 
divided upon the basis of mental age as superior, medium, and 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 13 


inferior. No correlations are given but it is stated that the 
superior group had the greatest initial ability as well as the high- 
est final efficiency, the medium and inferior groups following in 
their respective orders. 

Woodrow (1919:56) claims: “ What a child can do and how 
fast he can learn depends upon his mental age” (p. 37-8). 

L. S. Hollingworth (1920:21), after reviewing the experi- 
mental evidence at some length, supports the contention of Wood- 
row and others in the following statement: ‘‘ The feebleminded 
learn at the same rate, and in the same way as normal children of 
equal mental age, in tasks in which both have been experimentally 
tested’ (p. 186). 


CHAPTER III 
DESCRIPTION OF THE METHODS OF THE INVESTIGATION 


The Subjects: 


In accordance with the experimental aims already recorded, 
the subjects were selected upon the basis of intelligence or general 
mental ability. No additional selective agencies are known to 
have been involved other than those operative on all public school 
children. Racially the subjects were all of European descent with 
the exception of one girl who was included in ignorance in 
advance of the fact that she was partly of negro ancestry. 

In all, about 120 different subjects took part in one or more 
of the experiments. From fifty to sixty-five subjects were used 


in each experiment. Eleven took part in all three tests. These 


subjects were pupils in the seventh, eighth, or ninth grades of the 
University High School, Eugene, Oregon, the Lincoln Elemen- 
tary School of Oakland, California, or the Oakland High School. 
The experiments extended over the period from 1919 to 1922. 
The chronological ages varied around fourteen years as a 
mode.. The exact ages are recorded in Tables I, II, and III of 


Chapter IV.* Obviously it would have been desirable to have 


used subjects who were all exactly of the same age but the prac- 
tical difficulties of securing the requisite numbers at any one age 
made it necessary to sacrifice to some extent this theoretical 
advantage and attempt to allow for the influence of the chrono- 
logical age differences by resorting to the method of partial cor- 
relations as an approximation to the results which would have 
been obtained with a constant chronological age. 

The mental age range as shown by the same tables extends 

1 These tables have been omitted from this monograph because of diffi- 
culties in printing. They have been bound and placed on file in the 


Department of Psychology, Stanford University, California, and may be 
borrowed upon request. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 15 


from about eight to eighteen years, thus permitting a range of 
intelligence quotients of about 75 points. Tables V, VII, and IX 
of Chapter V present the data on the means and standard devia- 
tions of the age groups. The measure of intelligence used, the 
mental age, was that of the Stanford Revision of the Binet-Simon 
Scale. In every case at least one standard group test was used 
as a check on the mental ages obtained by the Binet tests. Where 
considerable lack of agreement was found, the subject was 
retested with the Binet tests and the results of the two tests 
averaged. The mental ages as stated in the tables are always 
those obtained by the Binet tests and are never based upon a 
group test alone. 

To avoid the problem of the possible influence of sex, the 
numbers of the sexes were kept roughly equal in all of the 
experiments. 


Description of the Tests: 
The three tests which were finally selected in accordance with 
the criteria already given will be designated as follows: 


I. Card Sorting. 
II. Code Substitution. 
III. Abstract Relations. 


A detailed description of each follows: 
I. CARD SORTING 


The task here consisted in sorting a pack of 100 cards bearing 
supposedly novel and meaningless designs into a case of ten com- 
partments arranged as two rows of ten compartments each. The 
following diagram will make this arrangement clear : 


16 


GILES MURREL RUCH 





Fig. 1.—Designs on Cards for Sorting Test. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 17 


The designs as printed here are full size. The compartments 
are, of course, greatly reduced. The dimensions of the case were 
12 x 28 inches and of the single compartments about 54% x 5% 
inches. The dimensions of the cards were 24% x 4% inches. 

The pack of cards consisted of ten cards each of ten different 
suits as determined by the ten designs shown above. The order 
in the diagram is that of their actual order in the compartments. 
Each compartment bore a label card corresponding to one of the 
designs on the cards. 

The instructions to the subjects were as given here: 


“Here is a pack of 100 cards. Each card has a design printed 
on it which is probably new to you. There are ten different 
designs and there are ten cards of each design. (E. shows one 
of the cards to S. for two seconds.) Under the cover here is a 
case with ten compartments. Each compartment has a label card 
and there is a compartment labeled like every kind of design on 
the cards. (E. raises the cover of the case for two seconds to 
allow S. a brief inspection. ) 

‘““When the signal ‘Go!’ is given, you are to take the cards 
one at a time and sort them into the compartments which have 
the same kinds of label cards. The black line is printed on the 
cards to show which is the bottom of the card and you should . 
take care to hold them with the black line down. The directions 
are to go as fast as you can without making mistakes. 

“Do you understand? Ready, Go!” (E. removes the cover 
of the case and at the same time starts the watch. The cover of 
the case is replaced as soon as the last card is thrown. ) 


The time was taken to the nearest one-fifth of a second. All 
errors and changes were noted by the experimenter. The num- 
bers of errors were surprisingly small, averaging fewer than one 
per trial per subject. Errors were finally ignored for lack of 
proper method of scoring. The arbitrary practice of adding one 
second to the time for each error, which has often been used, 
would not have affected the results to any significant extent. 

After the cards were sorted by the subject they were reshuffled 
by the experimenter in such a way as to avoid the occurrence of 
two cards of the same suit in consecutive order. Care was also 


18 GILES MURREL RUCH 


taken to avoid “runs” of cards in the same order from trial 
to trial. 

Each subject sorted the pack five times each day over a period 
of ten days (50 trials). The times for the five trials of each day 
were averaged as the daily score. 

An attempt was made to measure the improvement in the mere 
manipulation of the cards during the ten days of practice by 
having the subject “ box” a similar pack of plain cards five times 
before the first day’s regular practice and five times again at the 
close of the tenth day’s practice. These two sets of boxings 
were averaged and appear in Table I under the title of “ Initial 
Motor Time” (1.M.T.) and “ Final Motor Time” (F.M.T.), 
respectively. The boxing consisted in throwing the cards one at 
a time into the compartments taken in the order 1, 2, 3, 4, ete. 
The difference in the average initial motor time and final motor 
time was taken as a rough measure of the improvement in the 
mere manipulation of the cards. The value of this attempted 
measure will be discussed later. 

The practice series was usually continuous except for Sunday 
In a few cases both Saturday and Sunday were missed. 

Fifty-two subjects took part in this experiment. 


II. CODE SUBSTITUTION 


The second learning situation was that of transcribing a chapter 
from Oliver Twist which had been prepared in the code symbols. 
A second chapter of the same work was provided for translation 
into the code symbols. Each subject was given a key card bear- 
ing the code. This was kept before the subject during the prac- 
tice until such a time as its use was voluntarily abandoned. The 
key to the code is given herewith. 

The daily practice consisted of the translation for ten minutes 
from the code into English, followed by translation for the same 
amount of time from English into the code. Two minutes rest 
period was allowed between the two exercises. The total practice 
time was therefore twenty minutes a day. 

The score for each sort of translation was the number of letters 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 19 


(or symbols) transcribed correctly in the ten minutes. No addi- 
tional penalty was added for mistakes other than loss of credit 
for that letter or symbol. 





Fig. 2.—Key for Code Substitution Test. 


Sixty-six subjects took part in this experiment. Twenty-one 
continued after the regular ten day period for varying numbers 
of days. 

Samples of the test material will be found in the Appendix. 

The exact instructions to the subjects were as follows: 


“This test is one in which you have to translate a story written 
in a code or secret language into English words. You may have 
seen the code before in some of the tests which we have given. 
Whether you have seen the code before does not matter, as you 
will have a copy of the code before you as you work. 

“Now look at the key cards which I have given you and we 
will write a few words together so that you will understand how 
to use the code when we turn over the page and begin the real 
work. You watch the code as I write some words on the black- 
board. (E. writes ‘ University of Oregon’ slowly, pointing out 
each symbol on the key card.) 

“When the signal to turn is given, turn over the page and 
begin with the first code sign and write the English letter directly 
under it. Take the others in order and be sure that you know 
what each word is before you go on to the next. In this way the 
meaning of the story will often help you in the translation of 
the code. 


20 GILES MURREL RUCH 


“T am going to give you exactly ten minutes to work and I 
want to see how many words you can do in that time without 
making mistakes. Both speed and accuracy are important. 
The real purpose of this test is to see how much improvement you 
can make each day. For these reasons you should work just as 
hard as you can to make a good record every day. just as if you 
were playing a game. Remember, both speed and accuracy are 
important. 

“ Ready, turn, Go!” 


The following additional directions for the English code trans- 
lation were needed: 


‘““ Here you have to write the code word under the printed word. 
Since you cannot easily make the code letters as small as the 
printed letters, the lines only go half way across the page. You 


can write straight across the page beginning the line at the left. 
Ready, Go!” 


The code test was used as a semi-group test. The instructions 
and first day’s practice were given individually. Sometimes the 
subjects worked alone for two or three days. Usually, however, 
the subjects were formed into small groups of a half dozen after 
the first day. Judging from careful inspection this plan sacrificed 


little or nothing in the validity of the results, since any disturbing 


factors brought about by working in small groups were wholly or 
nearly wholly compensated for by the added stimulation of group 
competition. The experimenter checked up on this point by 
questioning the more intelligent subjects. In fact, it became the 
usual practice for the subjects to get together after the practice 
period and compare notes on their respective gains. 


Ill. ABSTRACT RELATIONS TEST 


The administration and nature of this test will be made clear 
by the instructions to the subjects which are given at length here. 
The introductory directions and explanations were necessarily 
very detailed and lengthy, due to the fact that the use of subjects 
with mental ages of eight or nine years made it imperative that 
every precaution be taken to insure the initial comprehension of 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 21 


the task. The hope was that failure to make a positive perform- 
ance in the test would indicate inability to solve the test problems 
after the instructions were understood and not merely lack of 
comprehension of these instructions. 

A key card was given to each subject and this was kept before 
him until voluntarily discarded. The key gives the clue to the 
nature of the problem. 


Key 
““C Is LARGER THAN A 
A IS LARGER THAN B 
B IS LARGER THAN D”’ 


“Tf we arrange the letters in the order of the largest to the 
smallest, they are: C-A—B-D. 


Samples 
—C plus D equals B (E. explains ) 
+ A minus B is less than C minus B % 
+ C minus B is larger than D 
— A minus D is equal to C 
+ B plus C plus D is larger than C plus A 
—A plus D is less than B minus C 
— B minus A is less than D minus C 


NOD Or B & DOF 


“The above samples are already marked correctly. Now begin 
with problem one of the regular test sheet and work the problems 
inorder. Be sure that you have answered each problem correctly 
before you go on to the next one. Mark those that are always 
untrue with a minus sign (—), those that are always true with a 
plus sign (+-), and those that might or might not be true with 
both a plus and a minus sign (+). You will be allowed to keep 
the key card before you at all times as you work. You will be 
told to stop at the end of fifteen minutes. Ready, Go!” 


In order to make as clear as possible the task to be performed, 
the experimenter demonstrated the solution of the seven samples 
on the key card as just given. E. said (verbatim) : 


“You have noticed from the key card that C is larger than A; 
A is larger than B; B is larger than D, so that if we arrange the 
letters in the order of the largest to the smallest, they are: 
C....A....B....D.. But, you must always remember that 


ae GILES MURREL RUCH 


you do not know how much larger C is than A, or A is than B, 
or Bis than D. All that you know is that C is larger than A, 
and A is larger than B, and B is larger than D. 

‘““ All of the letters stand for numbers that are more than zero. 
However, some of these problems do involve combinations of 
numbers that are equal to or even less than zero. Examples of 
these will be explained to you later. ; 

“There is one other point which you must remember or you 
will make mistakes. It is very important that you do not try to 
work these problems by letting numbers stand for the letters. 


These four letters do not stand for any certain numbers. For. 


example, if A were equal to 10, then C might be 11 in one 
problem and more than a million in the next. The same thing is 
true of all the letters. You do not know how large they are but 
only that they stand in certain order to each other as the key card 
states. You are sure to make mistakes if you try to substitute 
actual numbers for the letters. 

“Now look at sample 1. C plus D equals B. We would 
reason out the answer to this problem like this: since C is the 
largest of all the letters, it must be larger than B. If, then, we 
add D to C, we would make C still larger than B. The statement 
that C plus D equals B is always untrue, and it has been marked 
with a minus sign in front of it. The minus sign means that 
the statement never could be true. Do you understand? (The 
explanation is repeated in case the subject fails to comprehend. ) 

“Sample 2. A minus B is less than C minus B. In this sam- 
ple problem you will notice that the same number is to be sub- 


tracted from both sides of the problem. What number is it? | 


(Pause to see whether S. answers. Incase S. does not, E. con- 
tinues.) B is to be subtracted from both sides. Since this is 
true, we can ignore the B and we have left the statement that A 
is less than C. This is always true and it has been marked with 
a plus sign. 

“Sample 3. C minus B is larger than D. We know that C 
is always larger than D, but, if B were large enough, C minus B 
might be less than D. If, however, B is very small, C minus B 
might still be larger than D. Since we don’t know how large 
any of the numbers are, we can only say that the statement may 
or may not be true. It is marked therefore with both a plus and 
a minus sign. 

“Sample 4. A minus D is equal to C. We know that A is 
less than C. If now we subtract D from A it will be still smaller 


F 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 23 


than C. The statement must always be untrue and is marked 
minus. 

“Sample 5. B plus C plus D is larger than C plus A. In this 
problem which letter is found on both sides? (Pause as before 
for answers.) Since we are adding C to both sides we can 
cancel out the C and have left B plus D is larger than A. Both 
B and D are smaller than A. But, the sum of the two may be 
either larger, equal to, or smaller than A. We have marked it 
plus and minus because it may or may not be true. 

“Sample 6. A plus D is less than B minus C. Notice the 
expression B minus C on the right-hand side. Since C is larger 
than B, this must equal less than zero. A plus D is more than 
zero and hence must be larger than B minus C. It is therefore 
always untrue and has been marked minus. 

“Sample 7. B minus A is less than D minus C. This prob- 
lem is very much like the one before except that both sides are 
equal to less than zero. It is very much harder to decide which 
is the larger when both are less than zero. Numbers less than 
zero are called minus numbers and are something like debts. If 
Mr. A. has $150 and Mr. B. has $20, which is the richer man? 
(S. answers and E. accepts or corrects as before.) Now, if 
instead of having these sums of money, A. owes $150 and B. 
owes $20, which is the richer man? (S. answers as before.) 
This is why minus numbers are like debts, the larger a minus 
number appears to be, the smaller it really is. Minus 100 is less 
than minus 10, and minus 10 is less than minus 1, and minus 1 
is less than zero. Look again at sample 7. B minus A is less 
than D minus C. D is the smallest number of all and C is the 
largest. If we take the largest of all from the smallest of all, 
we have left a bigger minus number than if we took the next to 
the largest (A) away from the next to the smallest (B). But 
like a debt, the bigger a minus number looks to be, the smaller it 
really is. B minus A is larger, then, than D minus C and the 
statement is untrue. (The explanation is repeated once more if 
asked for. However, no further efforts to explain are made. ) 

“Now look at the directions at the bottom of the key sheet. 
You are to reason out these problems one at a time and mark 
those that are always true with a plus sign, those that are always 
untrue with a minus sign, and those that might or might not be 
true with both signs. 

“Remember two things: (1) Be sure that you are right 
before you go on to the next problem, and (2) do not substitute 


24 GILES MURREL RUCH 


numbers in place of the letters as you are sure to make mistakes. 
Ready, turn, go!”’ 


At first glance the instructions appear to be exceedingly 
involved. However, this was absolutely necessary in order to 
give the dullest subjects every possible opportunity to make prog- 
ress in the test. Zero scores could then be interpreted as failures 
to achieve rather than failure to comprehend instructions. The 
brighter subjects understood the instructions readily, or were even 
somewhat amused at the efforts to explain what to many of them 
was very obvious. A few of the subjects had studied algebra. 
The inclusion of a few subjects with mental ages below ten years 
who made zero scores was intentional in order that a close 
approach to the zero point in ability in this test might be had. 
In this case it should be pointed out that six subjects who failed 
to make better than a zero average score for the first five days 
were allowed to discontinue on the sixth day and their scores for 
all ten days recorded as zero. . 

The daily time limit was fifteen minutes. The test material 
for a given day consisted of 100 problems of the types repre- 
sented in the seven samples (see also in the Appendix). Three 
approximately equivalent sets of these were provided. Set I was. 
given on the first, fourth, seventh, and tenth days. Set II on 
the third, sixth, and ninth days. In case a subject continued 
longer than ten days, the same order of rotation of the forms was 
followed. 

Because the number of possible responses was limited to three, 
a correction for chance was necessary. This was done by the 
method of scoring the number right minus one-half the number 
wrong. Omissions were not counted either way. In case a 
subject completed the entire 100 problems of a set in less than 


the 15 minute time limit, his actual score was multiplied by 
15 


actual working time 
racy score’’ was obtained by dividing the number right corrected 
by the number attempted. An example will make the scoring 


This is termed his “ rate score.’ His “ accu- 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 25 


clear. Suppose a subject finished a series of 100 problems in 
12 minutes and 15 seconds with six omissions and ten mistakes : 


SKIES terre ada ane we ate 100 

C)eSIONS. tn core ter nae 6 

AttemptSity. mar vetide tees « 04 

iW FONDA eae teeta oe or 10 

Rightepen tas. fol 84 

R—W /2 79 
15 


Rate score = 79 + ———_= 96.7 
12.25 


Accuracy score =— = 84.0 


The speed score involves the assumption that the subject would 
have completed the estimated number had he continued for 15 
minutes on similar materials at the same rate of accuracy. 

Measured in time units, those subjects who finished in less than 
the time limit were less practiced at the end of the experiment 
than the slower subjects. In terms of the number of problems 
attempted, the rapid workers were more practiced at the end 
than the slower ones. Since so little is known of the comparative 
merits of time versus work units, it is wholly conjectural which 
group of subjects was favored by the plan adopted. 

More than sixty subjects took part in this experiment for at 
least ten days. The method was that of the semi-group plan 
which was described in the discussion of the code-substitution test. 

The subjects were not told their daily scores in any of the tests. 
If inquiries were made, answers of general encouragement were 
given. However, many of the subjects spontaneously tried to 
check up their gains by noting the number of test items attempted 
from day to day. No efforts were made to prevent the subjects 
comparing notes on their gains in this way. 


CHAPTER: LV; 
THE EXPERIMENTAL RESULTS 


The results of the three experiments have been recorded in 
Tables I, II, and III. Because of difficulties in printing, these 
tables have been suppressed in this report and have been placed | 
on file in the Department of Psychology of Stanford University, 
and may be borrowed upon written request. A brief character- 
ization of each table is given below. 

Table I gives the results for the fifty-two subjects used in card 
sorting. The daily scores are given as the averages of the five 
daily trials. Averages for the ten days of practice are also given, 
such averages including the entire fifty trials. Averages of five 
preliminary and five final ‘‘ boxings’”’ are also recorded. These 
have been described elsewhere. Table I-A, a supplement to 
Table I, shows the time scores for the first five trials separately, 
1.e., the five trials entering in to the average score of the first day. 

Table II presents the results for the code-substitution experi- 
ment. Daily scores are given in terms of the numbers of letters 
(or symbols) translated in ten minutes. Two figures are given 
for each day, the upper value being the code to English score and 
the lower the English to code score. A supplement to Table II, 
designated as Table II—A, gives the scores for a number of sub- 
jects who continued practice more than 15 days, in some cases as 
long as 40 days. . 

Table III presents the scores in the abstract relations test. 
Two daily scores are given for each subject, the upper being the 
“accuracy ”’ score and the lower the “rate’’ score. The descrip- 
tion of the computation and meaning of these measures has 
already been given in Chapter ITI. 

It is to be regretted that the full tabular statement of the 
original scores cannot be reproduced here. The reader will, 
however, experience little difficulty in following the statistical 
treatment, since the tables of Chapter V present the means and 
standard deviations of all subjects for all of the learning tests as 
well as for chronological age, mental age, etc. 


GHAPTER: *V- 
STATISTICAL TREATMENT AND INTERPRETATION OF THE RESULTS 


Two general methods were available in the treatment of the 
experimental data in order to reveal the part played by general 
intelligence in the rate of learning. The first of these is that of a 
division of the practicing group into two or three sub-groups upon 
the basis of the mental ages, e.g., into a “superior,” an “ aver- 
age,’ and an “inferior” group. The same sort of a division 
might also:-be made upon the basis of the intelligence quotients, 
e.g., those above 110, those from 90 to 100, and those below 90. 
The former has the advantage that it would be less open to the 
objection that the chronological ages of the subjects are not 
constant and hence the 1.Q.’s alone would introduce a variable 
factor from group to group. 

The second method which was open to use in the present study 
allows of even greater refinement in the corrections for the vary- 
ing chronological ages of the subjects. If the daily performances 
are correlated against mental ages, it is possible to eliminate the 
influence of chronological age by the use of the method of partial 
correlations. This necessitates the computation of all the pos- 
sible intercorrelations between the three variables, viz., mental 
age, performance, and chronological age. Substantially the same 
facts will be revealed by each method. The first has the advan- 
tage of being adapted to presentation in graphic form, the second 
of greater statistical refinement. For these reasons both methods 
will be used although the main treatment of the results will be 
based upon the method of partial correlations. 

In the computation of the coefficients of correlation the Pear- 
son product-moment formula was used in all cases. One general 
form of this formula is: 


‘ 


ZxrYy 





r= 
N 71 Fo 


28 GILES MURREL RUCH 


The probable errors of these correlations were obtained by the 


formula: 
j-r2 
P.E.r = .6745 


N 


The formula for the partial coefficients of correlation follows: 


Ty2—T1g3 Tog 


In order to secure a check upon the changes in the relative 
variabilities of the performances of the practicing group from 
time to time, the Pearson Coefficients of Variation have been 
computed for each day’s performance. These coefficients state 
the relative variabilities in terms of the ratio of standard devia- 
tions to the means. The standard deviation alone is a measure 
of the variability in terms of gross scores and hence is dependent 
upon the numerical magnitudes of the units of measurement. 
The formula for the Pearson Coefficient of Variation is: 


T19-3—— 





100 o 





Ve 
Mean 


Since the relative heterogeneity of the talent as represented by 
the daily scores is subject to change, such coefficients are of value 
in interpreting changes in the magnitudes of the correlation 
coefficients. 

As was stated in the introductory chapter, the selection of the 
tests finally used in the present study was an attempt to sample 
a wide range of possible learning situations. For this reason the 
initial correlations between performance and mental age present 
some interest as a check upon the wisdom of the original selec- 
tions. Table IV gives such correlations which have been selected 
from the larger tables which follow (Tables V, VII, and IX). 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 29 


TABLE IV 
Closeness of Relationship Between the Tests Used and General 
Intelligence. 
Test T 10.3 be) Oe. 
I Card sorting: 
ee ria le lanirstadavadcerntenieieleaceiire sar esse «loos warate 0.329 .083 
A Verdee Or citliale, HTSl Gay in. x ae. vis ss salva soe 0.176 091 
II Code substitution: 
(Code sie lish we anStea Vere te ae cc. hice eke 0.699 043 
Pie IG TOsCGtl Gs MERE CUA Vs. iighc tats os bis « Gokies ste Fad 0.666 .046 
III Abstract relations: 
RUALe CUESe ad UE re rset tees terete ae ce rele ae «6. 5 0.730 .040 
A CClita Gye (ES TiC a Vinee rests hates eke Fale Bee GLO eke she 0.800 031 


‘ P 


The notation “rie-3” refers here, as always, to the partial 
correlation between mental age and performance. when the 


influence of chronological age is eliminated. 


‘It will be seen from this table that ability to sort cards involves 
relatively little of the ability measured by tests of general intel- 
ligence. The mental processes involved in substitution abilities 
are much more closely related to general mental ability, as is 
shown by the moderately high correlations obtained. The mental 
functions involved in the solution of the problems of the abstract 
relations experiment can be said to be rather closely related to 
general intelligence as shown by the correlation of 0.800 + .031. 
These tests, then, do in some measure sample the range of mental 
functions with respect to the demands made upon intelligence 
from functions of very low relationship to functions of fairly 
close identity. It must be remembered that in view of the very 
large range of talent employed (see Tables VI, VIII, and X for 
the standard deviations of the mental ages), the exact magnitudes 
of these correlations have little significance. 

The chief interest for present purposes is not concerned with 
the question of the exact magnitudes of correlations of perform- 
ance and mental age, but rather with the evidence of systematic 
tendencies toward either increase or decrease of such correlations 
with practice. Tables V, VII, and IX present the partial coeffi- 
cients and the intercorrelations between the three variables for 


30 GILES MURREL RUCH 


each test. The notations of the variables by number are 


invariably as follows: 
1 Mental age. 


2 Performance. 
3 Chronological age. 
Tables VI, VIII, and X give the means, standard deviations, and . 
Pearson Coefficients of Variation for the separate variables in 
the different tests. . 
Table XI gives the correlations between initial and final per- 
formance in all of the tests. Initial performance refers to the 
score on the first day of practice and final performance refers to 
score on the tenth day of practice. 
In order’to interpret certain details of the experimental results 
which apply only to individual tests, each of the experiments will 
be discussed separately. 


TABLE V 


Correlations for Card Sorting 


Ist 5 Trials T40.3 

ieoy Hirat Ty Tig Tog M.A. and Score 
dayof M.A.and M.A. C.A. Independent of 

Practice Score and C.A. and Score C.A.(partial) N 


1 0.434 + .076 —0.379+ .080 —0.412 + .078 0.329: 083) eaz 

2 0.403 + .078 —0.379+ .080 —0.454+ .074 0.280 + .086 52 

3 0.192 + .090 —0.379+ .080 —0.348 + .082 0.069 + .093 52 

a 0.219+ .089 —0.379+ .080 —0.278 + .086 0.128 + .092 52 
0 


& OZ 0895 i083 79a 030m ORC 0OE I O85 3107 =*. 092458 
Days of 
Practice, 
i.e., averages 
5 daily trials 
1 0.310 = 1085 —0.379 = .080 —0.430 = .076 0.176 = .091 32 
2 0.058 = .093 —0:379 + .080: —0.402 = .078. —0.112 = .092 wae 
3 0.015 + .093 —0.379+ .080 —0.305+ .085 —0.114+ .092 52 
4 0.038 + .093 —0.379+ .080 —0.314+ .084 —0.092+ .093 52 
5 0.052 + .093 —0.379+ .080 —0.175+ .091 -—0.015 + .094 52 
6 0.014+ .096 —0.388+ .082 —0.188 + .093 —0.066+ .096 49 
7 —0.016+ .096 —0.388 + .082 —0.153+ .094 —0.083 + .096 49 
8 —0.077+ .097 —0.365+ .084 —0.201+ .093 —0.164+ .095 48 
9 —0.035+ .096 —0.365+ .083 —0.195+ .093 —0.117 + .095 49 
10 —0.060 = .096 —0.367 + .083 —0.041 + .096 —0.081 + .096 49 


Variables: 1. Mental Age. 
2. Score in Seconds. 
3. Chronological Age. 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 31 


TABLE VI 
Mean Scores, Standard Deviations, and Coefficients of Variation in 
Card Sorting 


first ig By As Pearson 
dayof Mean Mental Mean Chron. Mean Sele Coeff. 
Prac- Mental Agein Chron. Agein Score Score of Vari- 
tice Age Months Age Months inSec. inSec. ation N 
1 


13—9.1 26.9 S/d, 13.7 293.5 76.1 (Ay! Kee dey 
2 13-9 74 26.9 13—7.7 ils esy/ 195.5 49.7 PAs VA Waves 
3 13—9 71 26.9 V=—fed she 16225 35.8 SHAW 9 sie 
4 too et 26.9 1370/4 13.7 149.0 le YAEL GP 
5 ie) al 26.9 13—727 SAVE 140.8 ZOnd 18.96 52 
Days of 
prac- 
tice 
1 13—9.1 26.9 =f Saf 186.3 37.6 20.19 52 
2 13—9 ..1 26.9 1S ——Ja/ ey lilies 24.7 22 Lome, 
3 13——9r1 26.9 o—/ar Ses 104.7 Ziee 2022792 
4 139 31 26.9 1 / eh Asics 94.7 228%, 3 24/399 52 
5 13=—OrA 26.9 13—7.7 1Se7, 97.9 VATA) PAL EIA i oye 
6 1o——Ob Die 13—8.0 14.1 96.2 22.0 22.86 49 
7 13—9.1 Zi. 13—8.0 14.1 93.6 20.3 21.74 49 
8 13-—9),9 21.0 T3726 14.0 91.7 19.7 VAY es.) 
9 13—10:2 »§ 26.9 i375 13.8 92.4 2222 24.00 49 
10 T3=—1052598"20.9 13-725 13.8 93.3 19.9 20.31.5549 
TABLE VII 


Correlations for Code Substitution 
T12.3 
M.A. and Score 


Tyo ° 

Dayof M.A.and Tyg M.A. toa GA, Independent 

Practice Score and G.A% and Score OfeGoNs N 

Code to 

English 
1 QuG0e ce 049) 0.0448 083" 0.129 = = 082" 0,699 == 043) 66 
2 Wea oan 050cn——) 0440-8 G m0. 026i 0G 5me OL Ooo: 50 05000 
3 o/s 04655 — 0.044 085. 0.010 25 0835 0.070 <= 20460 66 
4 OOo ueta 049)" =. 0442 3085" —0-019 == - 083" 02635 7.04966 
5 RG Uopetae 052 -—0 4044 == 0835) —0, 012)=2 083," 0561 3i=E, 052." 66 
6 OFG3 Te 050 (— 07044 == 083, —0.2079 = - 082. 0:.630' 050 66 
7 RG / 2052 6) 0441-2" 0830 ——0.084 ee 083. 102613 27-052. 66 
8 0.683 + .044 —0.044=+ .083 0.041 = .083 0.686 .044 66 
9 GeGioree 054 = —() 023) 086 0.047 + .086 0.615+ .054 61 
10 0.608 = .056 —0.049 + .088 0.054 .088° 0.613 + .055 58 

English 

to Code 
1 Gnogor= 046.9 — 05044 229085) 7 —Or 0202s 4083.) 02 000=".040 st00 
2 eg 2050 me 0 044ee RG L0G Ieee 2 UO2o => O>0mE OO 
3 e509 053° ——02044 =e 083m —0. 057022 08379 059 7222053). 06 
4 O2520EE 7.060 *—0.044)=2 2083 =—02.028 = *..083>) 02520: 06066 
5 08513), 0615) —0.044 ==" 083) 1 —0075)=E 083s 05115 == 0618 166 
6 Osos 060) 0.044 == 5 083m 0036.28 083.0, 5302 2.060m.60 
7 GmO0 Ae SZ 0044 = 08 5e 0 0 LOL S500, /ueere oe ieOo 
8 0.582+ .055 —0.044 + .083 OL0PT 2 0830. 02083: 4.055 a. 00 
9 eo =e O0sme——0 O23 <= 080 0.027 + .086 0.520+ .060 61 
10 07576 ==.059) —0..049 ==". 088 ==—0. 029. == 3088" 07576 = .066 58 


SZ GILES MURREL RUCH 


TABLE VIII 


Mean Scores, Standard Deviations, and Coefficients of Variation in 
Code Substitution 
S:D; Sl): Pearson 
Day of Mean Mental Mean Chron. Mean SL Coeff. 
Prac- Mental Agein Chron. Agein Score Score of Vari- 


tice Age Months Age Months (Lett.) (Lett.) ations ae ae 


Code to 

English 
1 14—3.6 34.9 14—1.1 15.0 94.09 50.48 53.65 66 
2 143.6 34.9 14—1.1 15; 0. 9157288 a62. 85 39.81 66 
3 14—3.6 34.9 14—1.1 1520 °. 197. 274 269.83 35.42 66 
4 143.6 34.9 14—1.1 15.0°. \208.48>5.65.63 31.48 66 
5 14—3.6 34.9 14—1.1 1510 ON222342 ee 0a aS 29.95 2.66 
6 14—3.6 34.9 14—1.1 1520 2356630 ree 30.36 66 
7 14—3.6 34.9 14—1.1 ISO wZ4{e2ie akan 31.32 66 
8 14—3.6 34.9 14—1.1 1 255, Aa On 35.32 66 
9 144.8 35.0 14—1.3 1830 327035289504 32.94 61 
10 144.3 35.8 14—1.0 Lael 22/82202 0-902 oe 32.55, 38 

English 

to Code 
1 14—3.6 34.9 14—1.1 15.0.) 511068. 0655-85 50.49 66 
2 143.6 34.9 14—1.1 15,0 9153.64" 254-75 35.61 66 
3 14—3.6 34.9 14—1.1 15. Oc 5 176:07, 2261-92 35.05 66 
4 143.6 34.9 14—1.1 15.0) 4193.33. 22:62:53 32.34 66 
5 14—3.6 34.9 14—1.1 15.0,.4197.58. .761,8/ 3} .06. 665 
6 14—-3.6 34.9 14—1.1 15,0: 30208. 79 27 G7a7 32.46 66 © 
7 143.6 34.9 14—1.1 150° 218.48" 75234 34.48 66 
8 14—3.6 34.9 14—1.1 1 Ope cela ba Osea 36.61 66 
9 144.8 35.0 14—1.3 15.1 242.79 89.59 36.90 61 
10 14—4.3 35.8 14—1.0 bY naa’ tay Set YF 35.66 58 


I. CARD SORTING 


Table V shows definitely that intelligence’ offers but slight and 
temporary advantage in learning to sort cards. If the first five 
trials which make up the first day’s practice are alone considered, 
it appears that, even in the course of these five trials, the partial 
coefficients (column headed riz-3) decreased from 0.329 + .083 
for the first trial to 0.107 + .092 for the fifth trial. The value 
for the third trial is even lower, being 0.069 + .093. If the daily 
averages of the five trials are compared, it will be seen that these 
values fell from 0.176 + .091 on the first day to —0.112 + .092 


1 In the interests of concise expression, the term “ intelligence” has been 
used throughout this discussion as if it were a unitary or elemental factor 
or mental function. In reality no such definition is implied. For present 
purposes, no other definition is offered or needed than to point out that 
intelligence is here defined in terms of what the Binet tests really measure. 
Intelligence, therefore, is synonymous with Binet mental ages. 


ti alk) 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 33 


on the second day. The coefficients on subsequent days remained 
slightly negative but not significantly so in view of the large 
probable errors. 

The changes in the relation of chronological age to perform- 
ance is even more marked in degree. Starting with a correlation 
of —0.430 + .076 on the first day, the coefficients approach zero 
more and more closely each day, the final value being —0.041 + 
.096. In view of the negative correlation between the M.A. and 
the C.A. of the entire group (—0.379 + .080), the two sets of 
coefficients are quite in harmony with each other. 

One general fact seems evident throughout all of the correla- 
tions presented for card sorting, viz., that at the end of practice 
the subjects have arranged themselves within the group in an 
order which is quite independent of either their mental maturity 
or their age. This applies, of course, only within the limits of 
the age range represented in the experiment. Performance in 
card sorting, it can be concluded, is controlled by factors of a 


TABLE IX 


Correlations for the Abstract Relations Test 


T12.3 
M.A. and Score 


Ti2 
Dayof M.A.and T43 M.A. Tog C.A. Independent 
Practice Score and C.A. and Score or GAs N 
Rate 
1 Merc eee04 1 0.092 + .084 —0.060+ .085 0.730+ .040 63 
2 0.804 = .030 0.092 + .084 0.079 + .084 0.803 + .030 63 
3 0.819 + .028 0.092 + .084 OF 0532508 5a OFS 1S 0285.65 
4 0.786 + .032 0.092 + .084 0.034+ .085 0.787 + .032 63 
5 0.814 + .029 0.092 + .084 0.066+ .085 0.813 + .029 63 
6 0.789 + .032 0.092 + .084 0.096 + .084 0.787 + .032 63 
7 0.802 + .030 0.092 + .084 0.087 + .084 0.801 + .030 63 
8 0.815 + .028 0.092 + .084 0.107 + .084 0.813+ .029 63 
9 0.813 = .029 0.095 = .085 1.076. ..065..0;511 = ,02Z9" 62 
10 0.820 + .028 0.095 + .085 0.095 + .085 0.819+ .028 62 
Accuracy 
1 G7 952-032 0.092 + .084 —0.034+ .085 0.800+ .031 63 
2 0.712 = .042 0.092 + .084 0.008 + .085 0.714+ .042 63 
3 0.748 = .037 0.092 + .084 0203 522 085e0)3/748 39-03 72003 
4 0.817 = .028 0) 092-2 084 —0F 048.2085 0 820. 027 Oo 
5 0.829 + .027 0.092 + .084 O1017 se O85e5 0: 83h -es 0260.63 
6 0.833 + .026 0.092 + .084 0.015+ .085 0.8354 .026 63 
7 0.766 = .035 0.092 + .084 02035 = - 085% 0.766 22°, 026-763 
8 0.837 = .025 0.092 + .084 0.043 + .085 0.837% .025 63 
9 0.822 + .028 0.095 + .085 0.030 + .086 0.823+ .028 62 
10 0.842 + .025 0.095 + .085 0.006+ .086 0.845+ .025 62 


34 GILES MURREL RUCH 


TABLE X 


Mean Scores, Standard Deviations, and Coefficients of Variation for 
Abstract Relations 


SED: Mean S.D. Pearson 
Day of Mean Mental Mean soil SP Score Score Coeff. 
Prac- Mental Agein Chron. C.A.in in Prob- in Prob- of Vari- 
tice Age Months Age Months lems lems ation N 


Rate 
1 13—9.1. 33.5 13—6.6.. 7.05 20.04 15.48 115 25068 
2 13—9.1 33.5 13—6.6 .7.05 K on As 25.99 72:10 Go 
3 13—9.1 33.5 13—6.6 7.05 40.91 27:51 67-25" "63 
4 13—9.1, 33.5 13—6.6 7.05 42.54 31.84 74.85 63 
5 13—9.1 33.5 13—6.6 7.05 49.56 Vives 75.10 63 
6 13—9.1 33.5 13—6.6 7.05 55.48 Vipvay 67.63 63 
7 13—9.1 33.5 13—6.6 7.05 58.81 43.48 (3,90 40a 
8 13—9.1 33.5 13—6.6 7.05 65.95 44.50 67.48 63 
9 13—9.0 33.7 13—6.7 7.06 68.39 47.48 69.43 62 
10 13—9.0 33.7 13—6.7 7.06 69.68 49.28 70.72 62 
Accuracy 
1 13—9.1 33.5 13—6.6 7.05 40.12 24.65 61.44 63 
2 13—9.1 33.5 13—6.6 7.05 50.83 29.65 58. 33068 
3 13—9.1 33.5 13—6.6 7.05 52.98 29.09 54.91 63 
2 13-35-97 17033.5 13—6.6 7.05 48 . 33 29.15 60.31 63 
5 13—9.1 33.5 13—6.6 7.05 51.67 31.06 60 «i sGe 
6 13—9.1 33.5 13—6.6 7.05 51.43 29.24 56.85 63 
7 13—9.1 33.5 13—6.6 7.05 49.40 $1713 63.02 63 
8 13—9.1 33.5 13—6.6 7.05 51.19 29.72 58.06 63 
9 13—9.0 33.7 13—6.7 7.06 51.65 30.39 58.84 62 
10 13—9.0 33.7 13—6.7 7.06 50.02 31.64 63.257 Gz 


specific nature not related to general intelligence. That these 
specific factors show some tendency to be stable throughout the > 
course of the learning is shown by the correlation of 0.516 +.071 
(Table XI) between initial and final performance. This finding 
is quite in accord with the results of Wells, Hollingworth, Whitely, 
Chapman, Terman, Perrin, et al., previously cited. 

The transitory initial correlation of efficiency and intelligence 
presents especial interest because of the attempts of Gould and 
Perrin e¢ al., to define intelligence in terms of rapid initial adjust- 
ment to a learning situation. In Chapter II these authors were 
quoted as finding that in maze learning differences in the perform- 
ances of groups of varying intelligence were chiefly in evidence 
in the initial stages of the learning. These investigators found 
that their intelligent group (adults) made poorer initial records 
than the less intelligent group (children). Such findings are 
exactly opposed to the results given here for card sorting. It 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 35 


should also be objected that their use of adults and children as 
groups differing in intelligence alone, without reference to the 
other factors which must be involved in maze learning, is probably 
an unwarranted procedure. 

During the practice period, as shown by Table VI, the stand- 
ard deviations and the means of the time scores are reduced to 
about one-half of the initial size. This, however, does not 
involve any marked changes in the relative variabilities of the 
performances as is shown by the column of Pearson coefficients 
of variation, the first and tenth days giving almost identical values 


TABLE XI 


Correlations Between Initial Performance (i.e., first day) and Final 
Performance (i.e., tenth day) for Each of the Three Tests 


Test r JPN OY 
ROME TTT THOTT! TL r cic oy LG el sardioinhs & moe ees 0.516 .071 
II Code Substitution: 
GWodextopiin lish feo. aes ia.cee ee ects ane ete 0.606 .056 
EMSS CO MONE crt cn be tags « Riese R ew aLaalie bs 0.779 .035 
III Abstract Relations: 
Rat Oa, Cate eee A Be Rh Ne ad Ld 0.782 . 033 
A GCULAL VA Ate Oe a lininiis cea. avid sikehCee eve eheee 4 0.804 .030 


at 20.19 and 20.31, respectively. Change in the relative vari- 
ability of the practicing group, therefore, cannot explain the 
changes in the magnitudes of the correlations which have been 
noted. 

In order to determine, if possible, whether the absence of cor- 
relation between final performance and mental age was due to 
the fact that the subjects were nearing their limits of improvement 
and consequently the time scores were becoming more and more 
measures of the time given over to the purely motor processes of 
throwing the cards into the compartments, one further set of 
computations was attempted. The average time required for 
“boxing ”’ the cards five times on the tenth day of practice was 
subtracted from the average regular sorting time of that day. 
This difference, it was hoped, might be a rough measure of any 
elements in the total mental processes involved other than the 
purely motor functions. It was thought that any remaining 
sensory processes in the learning which had been obscured by the 


36 GILES MURREL RUCH 


motor factors might thus be separated out from the total time. 
The difference between the final sorting time and the “ boxing ”’ 
time has been termed “ Difference Time.” Correlations of this 
time with mental age and the partial correlations of these two 
variables excluding chronological age are given in Table XII. 


TABLE XII 
Correlations of Intelligence and “ Difference Time” 
2 3 
M.A. OPTI C.A. 
pe. BY, UC ey as ee ee UN Se iby 0.055 + .096 —0.367 + .083 
yaa ial ee ated Aaya OF055 st 0G st ck Ratu ee —0.149 + .094 
i ie Ge. ey deg —A) 367 083° —0. 1490948 ee ea eee 


15-3 = 0.0004 = .0964 
It will be seen at once that this ‘‘ Difference Time” proved of 
no significance as far as its relation to intelligence is concerned. 
This conclusion is identical with that of Brown (1914:6), who 
reported a similarly attempted measure as invalid. 


II. CODE SUBSTITUTION 
The situation with respect to the code test is quite different 
from that in card sorting. Tables VII and VIII give the data on 
correlations, central tendencies, and variabilities. In both types 


of substitution, 7.e., code to English and English to code, we find — 


moderately high initial correlation with mental ability. The 
partial coefficients on the first day are 0.699 + .043 and 0.666 + 
.046, respectively. Both sets of correlations drop slightly during 


the course of practice. Nevertheless, the decrease is probably not 


very significant in comparison with the probable errors.” The 
partial correlations on the tenth day are 0.613 + .055 for code 
into English and 0.576 + .060 for English into code translation, 


the correlations are even lower on intermediate days, e.g., 
0.511 + .061 on the fifth day and 0.520 + .060 on the fourth day. 


2 By means of the formula for the probable error of a difference, it can 
be shown that obtained differences in order to be very significant would 
have to be as large as .25 or larger. This formula reads: 

P.E. (Diff.) =V P.E2, + P.E.2,. 
This will give values for the P.E. of the difference around .085 where the 
P.E.’s of the r’s are .06. The usual interpretation is that of calling differ- 
ences uncertain unless the difference is at least 3 times its probable error. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 7 


The decrease in the magnitude of the correlations between per- 
formance and intelligence is relatively slight and the indications 
are that the onset of automatization of the mental processes 
involved would be very much delayed in comparison with card 
sorting. 

The question might be raised again here whether the fall in the 
size of the correlations (which seems to be most marked from 
the first to the second day) is merely the result of the decreased 
variability of the performances of the subjects on the second day 
as compared with the first, as shown in Table VIII. It is true 
that the relative variabilities do decrease sharply from the first to 
the second day, viz., from 53.65 to 39.81 for code to English and 
from 50.49 to 35.61 for English to code. It is further to be 
noted that after the second day there is comparatively little change 
in the relative variability of the subjects. Against this possibility 
can be urged the fact that the correlations are practically as high 
on the third and eighth days for code to English as they were at 
the outset, and yet their Coefficients of Variation are smaller in 
about the ratio of 53:35. Similar results will be found to hold 
true of English to code translation, the fluctuations in the sizes 
of the Pearson Coefficients of Variation seem to be little related 
to fluctuations in the correlation coefficients. Most of these 
minor fluctuations are not significantly large in comparison with 
the probable errors of the coefficients of correlation. 

Attention should be drawn to the fact that the range of talent 
is greater in the subjects practicing with the substitution test than 
was the case in the card-sorting test, the standard deviations of 
the mental ages being, respectively, about 35 and 27 months. 
This difference in the spread of the talent had operated naturally 
to increase the relative difference between the amount of correla- 
tion found between intelligence and card sorting, on the one 
hand, and intelligence and substitution ability on the other. The 
range of talent in the subjects used for card sorting is probably 
not very dissimilar to that ordinarily found within a single school 
grade but is much greater than that of a single grade for the 


substitution test. 


38 GILES MURREL RUCH 


As shown by the correlations between initial and final ability 
in the code test (Table XI), the subjects maintain their relative 
positions with great fidelity, the correlations being 0.606 + .056 
for code to English and 0.779 + .035 for English to code. This 
constancy is considerably greater than was found for card sorting. 

In general the fall in the correlations during practice is greater 
in the case of the English to code than in the reverse type of trans- 
lation. The reason for this is not entirely evident. It might be 
attributable to the influence of the value of the use of the context 
in translation of code into English, upon the assumption that the 
context is a function analogous to comprehension ability in reading 
and hence offers greater opportunity for the operation of intel- 
ligence, or it may be purely a chance phenomenon. There is no 
experimental evidence which can be cited in proof or disproof of 
this hypothesis. 


III. ABSTRACT RELATIONS TEST 


In this test we find a different situation with respect to the 
influence of intelligence than in either of the two preceding experi- 
ments. As shown by Table XI, the initial correlations between 
mental age and performance are high; the partials excluding the 
influence of chronological age differences being 0.730 + .033 for 
rate and 0.800 + .030 for accuracy. 

In the main, practice seems to increase the correlations slightly, 
especially in the case of “rate” (Table IX). The situation with 
respect to “accuracy” is less certain in its interpretation. By 
reference to Table X it will be seen that the mean daily scores for 
accuracy did not increase appreciably. From the first to the 
second day there was a noticeable increase, 40.12 to 50.83, but 
subsequently the means are almost constant. This was an 
unforeseen difficulty and one which has probably affected the 
results of this test very considerably. The interpretation of this 
situation is undoubtedly to be had in the fact that, during the 
course of the practice, the subjects, in the main, failed to learn to 
solve any more new types of problems. A given type of problem 
was either within the ability of the subject at the outset of the 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 39 


practice or it never became possible for him to make the solution. 
The improvement, then, perforce, had to come in the direction of 
the increased speed of solution of the same types of problems with 
added practice. As is well known, rate scores are less dependent 
upon intelligence than are accuracy scores, at least for mathematical 
abilities. 

It should be further pointed out that the rate score includes 
the factor of accuracy as well as rate proper (see Chapter III), 
and is therefore the better single measure of performance. 

The relative variability of the daily accuracy scores remains 
practically constant save for minor fluctuations which are not 
constant in direction. This is equally true of the rate scores 
where improvement is marked. 

That the curves of the individuals, if plotted, would not cross 
to any considerable extent is shown by the correlations of the first 
and tenth days’ performances. These were 0.782 + .033 for rate 
and 0.804 + .030 for accuracy. 

All of the evidence considered, practice in the solutions of 
abstract problems has not decreased the amount of correlation of 
this ability with intelligence, and probably such correlations tend 
to increase with practice within the time limits of the experiments. 


GENERAL CONSIDERATIONS 


The individual characteristics of the learning processes involved 
in the three separate tests employed in the present investigation 
have been discussed at sufficient length in the preceding pages. 
There yet remains the task of bringing the specific findings 
together into generalizations regarding the role of intelligence in 
conditioning learning. 

The most striking conclusion which can be drawn from these 
investigations is that it is impossible to generalize about the form 
of the learning curve im toto. We can speak of learning curves 
in the plural sense, but there seems to be no reason to assume that 
there exists any one type of learning curve which has universal 
validity regardless of the mental functions which may be involved 
and independent of those differences of innate capacity which we 


40 GILES MURREL RUCH 


term intelligence or general mental ability. No doubt there are 
certain characteristics of learning curves which are common to all, 
such as rapid initial rise, followed by flattening, and final gradual 
approach to the physiological limits of improvement. What is 
meant by this categorical denial of any one generalized form of 


the curve of learning is that evidence has been here presented’ 


which suggests at least two important controlling factors in the 
rate of learning. These two factors are: 

(1) The type of mental function undergoing exercise, and 

(2) The mental level of the subjects used. 


These issues must also be stated in terms of the problem of 
the increase or decrease of individual differences under practice. 
Reference has already been made to the fact that the whole 
matter of individual differences in learning capacities has never 
been subject to agreement. Specifically, we can refer again to 
the findings of Binet that individual differences tended to be 


effaced with practice, at least for such simple tasks as cancellation 


tests of various types. Spearman and Kruger have already been 
quoted to the contrary in their refiguring of Oehrn’s data on 
continued adding. Burt’s results were inconclusive in the main 
and cannot be held to support either contention. On the other 


hand, Thorndike has adhered firmly to the conviction that those ~ 


differences present in performance at the outset due to man’s 
original nature are markedly increased by continued exercise. 
Thorndike would corroborate the work of Spearman and Kriiger 
and oppose the position taken by Binet if these findings are 
accepted at face value without further analysis. 

In the light of certain new data which have been presented 
here, however, it is perhaps possible to reconcile these divergent 
opinions in considerable measure. These opposed conclusions 
have probably not taken into account sufficiently the first of the 
above mentioned factors which have been emphasized in the 
present study, viz., the effect of the type of mental function 
undergoing exercise. Binet’s tests were almost entirely of the 
cancellation type, and it is now well established that such tests 
involve relatively simple mental processes. The work of Thorn- 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 41 


dike and his students was almost entirely concerned with relatively 
complex functions such as mental multiplication and adding. 
The same holds true for the study of Spearman and Kriger. 
Moreover, considerable new evidence has been presented in the 
present discussion which serves to show that both conclusions are 
probably correctly drawn for the materials used, and that the real 
error involved is merely that of overgeneralization from a too 
restricted sampling of mental processes concerned in the learning. 
In order to examine this general hypothesis more specifically 
and from several possible angles, the general issue can be divided 
into at least three more sharply defined questions. These are: 


(1) 


(2) 


(3) 


The question of the changes in the relative variabilities of 
the entire practicing group, t.e., tendencies for the ratio of 
standard deviation to the mean to change from day to day 
during the practice. Such ratios are found in the Pearson 
Coefficient of Variation. 

The problem of the increase or decrease of the individual 
differences in performances in terms of absolute increments 
when the practicing group is subdivided into a “superior,” 
an “average,” and an “inferior’’ group upon the basis of 
mental age. 

The question of the fate of correlations between mental age 
and performance during continued practice. 


The changes in the relative variability of the entire practicing 
group have been indicated by the Pearson Coefficients of Vari- 
ation as given in Tables VI, VIII, and X. In the case of card 
sorting the relative variability of the group became rapidly less 
in the first five trials, being 25.93 for trial 1 and falling to 18.96 
for the fifth or last trial of the first day of practice. However, if 
we consider the average daily scores, there is no constant tendency 
toward change in either direction. The group as a whole repre- 
sents a condition of no change in relative variability under prac- 


tice. 


The rather rapid change within the first five trials is a very 


transitory phenomenon, and it must be pointed out that the single 
trials are much less reliable than the daily averages, and hence are 


42 GILES MURREL RUCH 


not strictly comparable to such averages. The chief significance 
of this stability of the Pearson Coefficients of Variation is prob- 
ably that they offer evidence that changes in the correlations of 
mental age and performance are little affected by changes in 
relative variability from day to day. 


In the case of the code substitution test, the situation with’ 


respect to relative variabilities is slightly different. In both 
kinds of substitution, there is a marked decrease in the variability 
from the first to the second day, and little change subsequent to 
the second day. This change amounts to a difference of from 
53.65 to 39.81 for code to English, and from 50.49 to 35.61 for 
English to code. Again, variability in the relative sense here 
implied cannot be a factor in change in the magnitudes of the 
correlations of intelligence and performance. 

Finally, in the case of the abstract relations test there is even 
less change in the magnitudes of the Coefficients of Variation. 
For reasons already stated, the rate scores are the better single 
measure. Although the coefficient for the first day is slightly 
greater than on any other day, it is almost equalled on the fourth 
and fifth days, and the differences are probably not significant. 
In the case of accuracy there is absolutely no reason to believe 
that systematic tendencies toward change are present in either 
direction. 

Taking all three tests together, the relative variabilities are 
surprisingly constant over the period of ten days of practice. In 
the first two tests it would appear that there exists a relatively 
short period in which the members of the practicing groups tend 
to arrange themselves in a somewhat more homogeneous manner 
in their individual performances, but that this is a very transitory 
phenomenon. 

In order to discuss the second of the problems to be considered, 
viz., that of the increase or decrease of the differences between 
the three subgroups classified as “ superior,’ “ average,’ and 
“inferior,” certain new data must be introduced. These three 
groups were formed by breaking the total group into the highest, 
middle, and lowest thirds taken in the order of their mental ages. 


— pe 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 43 


For the three tests the divisions were as follows. The numbers 
correspond to those assigned to the subjects in the tables of the 
raw data. 


Card sorting Code Abstr. Rel. 
WOUDEHION a | PTOUDE slo ack’ Nos. 1-17 Nos. 1-22 Nos. 1-21 
MEAVEtAsemie LOUD ies: ose “18-34 23-44 “22-42 
“daterior” groupsiiis ies be “35-52 “45-66 “43-63 


Tables XIII to XV and Graphs I to V show the mean scores 
of each of these three groups during each day of the practice. 

In the case of card sorting, there is a very marked tendency for 
the groups to draw together, 1.¢., to lose the differences present at 
the outset. This is most rapid during the first five trials. By 
the second day the three groups have lost their separate identities. 
In the case of the abstract relations test we find the reverse situ- 
ation with respect to the absolute gains. In terms of absolute 
increments the three groups are constantly increasing those dif- 
ferences present in the initial stages of the learning. The curves 
diverge like a fan. These two tests tend, then, to show opposed 
tendencies toward convergence or divergence. In the substitution 
test we find the curves to be rather irregular. However, if the 
same were smoothed until they approximate best-fitting lines, the 


TABLE XIII 


Average Time Scores in Seconds for the Superior, Average, and Inferior 
Groups in Card Sorting 


Trials of Superior Average Inferior 
First Day Sec. N Sec: N Sec. N 
1 261.4 17 280.8 17 336.7 18 
2 176.1 17 189.3 17 218.6 18 
3 153.1 17 161.4 17 169.4 18 
4 139.6 WA 150.6 17 P5527 18 
5 134.3 17 140.9 17 146.9 18 
Days of 
Practice 
] t/a3) 17 182.9 17 201.6 18 
2 111.8 17 109.8 17 117.8 18 
K 101.8 17 108.9 17 103.9 18 
4 95.7 17 99.0 17 10172 18 
3) 93.2 17 102.6 17 97.7 18 
6 94.2 16 101.0 16 95.2 17 
7 90.3 16 99.6 16 90.9 17 
8 89.0 16 98.5 16 87.6 17 
9 89.8 a7 97.1 16 90.8 16 
10 88.8 17 95.9 16 86.7 16 


44 GILES MURREL RUCH 


separate curves of the three groups of subjects would be roughly 
parallel. 

The whole range of possibilities in the forms of the learning 
curves for groups classified upon the basis of mental age can be 
represented hypothetically by Diagram I which is given here. 
Type I represents convergence of the curves or decrease of differ- 
ences in gross improvement under practice. The card-sorting 
experiment illustrates Type I. Type III presents the situation 
found to obtain for the abstract relations test. Type II is not 
exactly represented in our findings, but is theoretically possible, 
and there is some evidence that the code test approaches this type 
to some extent. 

The third of our three problems is concerned with the fate of 
correlations between performance and intelligence. It bears cer- 
tain similarities to each of the other issues which have just been 
discussed. It has been repeatedly pointed out that changes in the 
relative variabilities of the practicing group may influence the 


TABLE XIV 


Average Daily Scores in Code Substitution for the Superior, Average, and 
Inferior Groups of Subjects 


Day 
Code to Superior Average Inferior 
English Lett. N Lett. N Lett. N 
1 134.0 22 102.3 22 59.8 22 
2 193.4 22 167.5 22 110.7 22 
3 244.3 22 203.7 22 141.9 22 
4 254.6 22 206.0 22 162.0 Ze, 
5 270.2 22 212.2 22 184.6 ee 
6 291.0 ae 222.4 22 195.5 22 
7 306.4 22 237.8 22 195.6 ae 
8 329.5 22 246.2 22 189.6 ae 
9 336.8 22 ZOOL, 19 213.0 20 
10 346.8 wh 256.9 7 es 222.4 20 
English 
to Code 
1 149.0 22 114.9 fips 67.4 22 
2 187.5 Ze 163.0 22 tes 22 
3 215.6 22 183.9 22 133501 22 
4 226.7 22 194.9 22 156.8 22. 
5 235.4 22 189.3 22 16723 2a 
6 248.4 tp 200.3 22 174.8 22 
7 274.0 22 215.0 22 172.9 22 
8 28145 22 224.8 Ze 173.9 22 
9 301.6 22 229,0 19 185.5 20 
10 ayer 21 232.6 17 206.8 20 


s 
3 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 































































































































































































7 


























































































































































































































Fig. 3. 










































































46 GILES MURREL RUCH 


magnitude of such correlations because of increase or reduction 
of the range of talent involved. However, the fact of relative 
constancy of such relations in all of the tests, at least after the 
brief initial period, eliminates this factor in the main. 

It is, of course, entirely possible, theoretically, that a practicing 
group can maintain the same relative variability as measured by 
the ratio of standard deviation to the mean, and yet the individuals 
composing the group will be found to approach more and more 


TABLE XV 


Average Daily Rate Scores in the Abstract Relations Test for the Superior, 
Average, and Inferior Groups of Subjects 


Day of Superior Average Inferior 

Practice Prob. N Prob. N Prob. 
1 33.9 21 16.4 21 8.8 2) 
2 63.8 21 27.6 21 14.2 21 
3 68.4 21 R09 21 16.6 ef | 
4 75.4 21 34.5 21 20.9 21 
3 88.4 21 41.8 21 2234 21 
6 92.7 21 42.8 21 27h2 21 
7 101.7 21 46.6 21 Dass 21 
8 110.6 21 6275 21 31.9 21 
9 116.8 21 53.6 20 v2.8 21 
10 118.5 21 CY py 20 30.2 21 


closely to the order demanded by their separate degrees of general 
mental ability. The reverse of this condition is also possible, 1.¢.,. 
the subjects may day by day lose more and more the relation of 
their performances to their mental abilities. This, in fact, is 
what would probably tend to happen where some correlation exists 
between intelligence and performance in the initial stages of the 
learning but where automatization sets in rapidly with the result 
that great changes in the mental functions brought into play in 
the learning take place during the course of the practice. This 
point has been repeatedly brought out in laboratory studies. 

In general we can expect any one of three situations to be 
found with respect to the fate of correlations between intelligence 
and learning : ; 


(1) Decrease in the size of the coefficients of correlation from 
day today. If the relative variability of the entire practicing 
group is constant, this means that the individuals tended to 


Time in Seconds 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 47 


arrange themselves in their performances in the relative 
orders suggested by their mental ages at the outset, but that, 
from day to day, these same individuals became rearranged 
in orders which were quite or almost unrelated to general 
intelligence. Individual differences would still be found in 
the same relative degree as before, but intelligence would 











































































































































































































































































































am i 
= 
te 1. | 
| 
| 2 ee 
Tal tt a Fat Da f 
i coo ot 
+} 54. 
Resend na ESESUECaGESeeSErs | | 
1 iar TIBI Ga aaa | 
ene Ho i { aes 
SIS e Gna e Bh tot jt tt t ; im aa ‘D SeES CUT Tt 
H THANE | rH Eeeeee EH aaa HH 
a | dO Oe a a ek ma 
Pty { ry 
| chi a 
T T ae 3 H 
i =a 
ty 
el Zang 
1 if 
i | } 
i Pots 
















































































Fig. 4. 


48 GILES MURREL RUCH 


not longer be a factor in controlling the positions of the 
subjects within the group. 

(2) The coefficients of correlation might remain constant from 
day to day. Changes in position of individual members of 
the group would still be possible, but these changes would 
probably be relatively small in extent and not constant in 
direction with reference to the order demanded by the mental 




































































































































































Time in Seconds 


Day 1 g 3 4 5 6 fi COLO 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 49 


ages of the subjects. As before, the relative variability of 
the group as a whole might remain constant. 

(3) The correlations between performance and mental age might 
be found to be increased with practice. Here again the 
relative variability of the entire group might not change from 
day to day, but the individuals composing the group would 


eT 
YO Pa 



















































































50 GILES MURREL RUCH 


be found to be approaching more and more closely the order 
demanded by their mental ages. 


These three possibilities are admittedly hypothetical in part. 
Each carries with it certain further corollaries. One of these is 
the question of correlation between initial and final performance. 

































































CCCCC pia 
Seeeee 20am ccc 
































































































Ty 
2 408 4eee rt 
Attar Try 
Sel Fann 4a 
<< 4Gne 


aSeee 
B= SRGRR EERE Bee e Us 













































































INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 51 


The first situation demands a relatively lower correlation between 
the positions of the subjects at the start and at the finish of 
practice. The curves of individual subjects are likely to cross 
and recross toward the end of practice. However, loss of ail 
correlation between mental age and performance is possible with- 











BET SSSESESESSESEEE 














Bae wa ae a 
dare pe tb) areas 
eo St eile 








Avera ca 
Banesteescesesteessces 
ipetnee? 
abu 











































































































ss sivesitositniit 









































SHodonsoveusastassnsantevectestosd ovendassaventosessestessssantasestertertatast? 


52 GILES MURREL RUCH 


out loss of correlation between initial and final positions. This 
is shown by the card-sorting test where the initial correlation of 
intelligence and performance rapidly fell to zero although the 
correlation between the performances of the first and last days 
was 0.516+ .071. Crossing of the individual curves would 
probably be slight in the second situation, 7.e., where the correla- 
tions of performance and intelligence are practically constant. 
The amount of crossing of individual curves, or what is the 
same thing, the amount of correlation between initial and final 
performance, would seem to be controlled by two general factors: 


(1) Individual characteristics in the improvability of the particu- 
lar mental function undergoing exercise. These character- 
istics would be subject to individual differences in different 
human beings. This would be individual learning capacity 
in a mental function per se. Such individual differences 
might conceivably be quite unrelated to the differences exist- 
ing among the same human beings with respect to intelligence 
or general capacity for learning. An illustration might be 
found in the learning to control a baseball by a pitcher. If 
we assume for the sake of discussion that this is a function 
entirely unrelated to intelligence, a learning capacity for 
throwing a baseball accurately might be relatively constant 
for a given individual and at the same time great individual 
differences in this power could exist. A moderately high 
correlation between initial and final ability in this act might 
be entirely possible. The learning curves of such individuals 
would not cross to any considerable extent. In fact, this 
situation is realized to some extent in the card-sorting experi- 
ment where the initial performance correlated with the final 
performance to the extent of 0.516 + .071, but after a very 
brief initial period the performances on successive days were 
quite unrelated to intelligence. Individual differences were 
still as great as before in relative terms. 

(2) This first factor would be subject to modification by a second 
factor, viz., the general mental abilities of the subjects. 
This is really a distinction of the nature of that sometimes 
assumed by psychologists in the discussions of general versus 
specific factors in talent. In the case of card sorting, intelli- 
gence does not appear to exert any influence upon the posi- 
tions of the subjects in their relative orders of efficiency 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 53 


after the very first few trials. On the other hand, if we 
consider a complex function like the abstract relations test 
or even the code test, we find that intelligence is constantly 
operative in determining the efficiency of the performance. 
Since intelligence is a constant factor, 1.e., does not change 
in the course of the experimentation to any significant extent, 
it should act to supplement the specific factors making for 
constancy of relative position from day to day, and, on the 
whole, correlations of initial and final positions might be 
found to be higher than in those cases where only the specific 
capacities are concerned. The actual correlations for the 
first and last days’ scores in the code test were 0.606 + .056 
and 0.779+ .035 for code into English and English 
into code, respectively. For rate in abstract relations the 
coefficient was 0.782 + .033 and for accuracy 0.804 + .030. 


If both of these factors are varied in opposite directions such 
as might be the case with a learning situation presenting zero 
correlation with intelligence at the outset and rising to perfect 
correlation (1.00) at the end of practice, we would obtain the 
maximum of crossing and recrossing of the separate curves of 
different individuals, together with zero correlation between 
initial and final positions. This example may not be a real one 
in the sense that it corresponds to any psychologically possible 
situation. Its introduction is made purely for the purpose of 
setting the distinction between the specific and general factors in 
learning into the sharpest possible contrast. Whether such a 
situation is ever possible is very doubtful. 


Comparison of the Present Results with the Work of Certain 
Other Investigators: 

In Chapter II, devoted to the review of the literature related to 
the present problem, several references were made to conflicting 
results and interpretations in the experimental studies of learning. 
In part, these issues have been discussed as our new data were 
presented. However, several of these questions have not been 
thrown into orientation with present results. In some cases it 
has been possible to reconcile differences of opinion; in others, it 
will be necessary to leave the differences standing in opposition. 


54 GILES MURREL RUCH 


The suggestion was previously made that the apparent contra- 
diction between the work of Binet with cancellation tests and 
that of Spearman and Krtiger and of Thorndike on continued 
adding and other arithmetical functions has resulted from the 


fact that they were comparing mental functions which are widely » 


different. When this factor is recognized, our present findings 
can be held to harmonize the two positions up to the point of 
rejecting the universality of their generalizations. On the other 
hand, Jones (1917:13) has been quoted to the effect that, in his 
opinion, the work of Wells, Chapman, and Hollingworth was 
opposed to the general conclusions of Thorndike. Jones bases 
his argument primarily on the fact that Wells found that those 
subjects who gained most in adding over a period of thirty days 
did not gain the most in cancellation during the same period of 
practice. Upon the assumption that card sorting is similar to 


cancellation in its demands upon intelligence and that the solution | 


of problems like our abstract relations problems involves abilities 
roughly comparable to those of continued adding, the fact of 
differential gains in Wells’ two tests presents no serious difficulty 
in its interpretation. In our card-sorting test, the dull subjects 
gained most and the bright ones least. In the abstract relations 
test, the situation was reversed, the bright ones gained most and 
the dull ones least. Our results, then, are in harmony with those 
of Wells. Again, the apparent conflict need not be accepted as 
real but can rather be attributed to failure to recognize the fact 
that learning curves vary markedly in form for various types of 
mental functions. . 

However, when we consider the differences in the results 
obtained for correlations between initial and final abilities, it must 
be admitted that present results are not entirely in harmony with 
all of the previous work. ; 

Hollingworth (1914:29) reported correlations between initial 
and final abilities for six tests with thirteen adult subjects, as 
follows: 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 55 


AGRI, deiitetiateliilh waste oes eR 15 
CD DOSIFES Pete ks oe ee ere —.08 
Olt ANA oh. Beere ae .68 
DISChImMINAtOMie: maslsc eo ees .68 
(Ancellatignin sei a At se ete 67 
Goordinationgs re: Ss Fee ee 52 
BIbE DITK ete ea: ia et Ales ok Cee ere 25 


The values obtained for adding and opposites are strikingly 
different from those reported for the higher mental functions in 
the present investigation. In opposition to these figures by 
Hollingworth are Chapman’s results (1914:9). The latter found 
correlations of initial and final performance of .59 for opposites, 
.96 for addition, .87 for multiplication, .87 for color naming, and 
.75 to .85 for cancellation. 

Neither of these sets of results can be compared directly with 
those obtained here. In the first place, Hollingworth’s subjects 
continued their practice for 175 trials. As Hollingworth himself 
has pointed out, the tests underwent great changes in their psycho- 
logical characteristics during the course of practice. Moreover, 
the subjects were but thirteen in number in Hollingworth’s study 
and but twenty-two in Chapman’s investigation. All were adults. 
Exactly the same words were used in each practice period although 
the order of presentation was changed. The conditions, there- 
fore, were favorable for rapid automatization and marked 
decrease of intellectual demands from day to day. Nevertheless, 
it must be admitted that there is a considerable disagreement here 
which cannot be explained at present. 

Whitely (1911:54) found correlations between starting point 
and gain to be equal to about .50 in such functions as cancellation, 
discrimination of weights, sorting, and the pencil maze. As has 
been stated, these results are out of harmony with certain of 
Whitely’s other work as well as with the present study. In our 
card-sorting experiment the subjects making the poorest initial 
records gained most during practice, a fact which would demand 
negative correlation. Thorndike has called attention to the fact 
that Whitely’s scores are not very reliable because they were 
obtained from only nine subjects. 

It is unnecessary to enumerate the many other minor disagree- 


56 GILES MURREL RUCH 


ments in the literature of the psychology of learning. Enough 
evidence, it is thought, has been presented in the present paper, to 
indicate clearly that important generalizations concerning learning 
capacities must distinguish the separate roles of general intelli- 
gence and the complexity of the mental functions involved, in 


addition to those specific factors governing changes of efficiency - 


during practice. 


CHAPTER VI 


SUMMARY AND CONCLUSIONS 


The main conclusions which have been reached in the course 


of the present experimentation are as follows: 


iy 


There is no reason to assume that there exists any one type 
of learning curve which is independent of : 
(a) The type of mental function which is undergoing 
. practice, and of 
(b) Differences in the general mental abilities of the sub- 
jects undergoing the practice. 


With respect to the second of these two factors, 1.e., general 


mental ability, correlations between performance in learning 
and measures of general intelligence are subject to any one of 
three possible fates: 
(a) Such correlations may decrease from day to day as 
was the case with card sorting, or 
(b) Such correlations may remain practically constant 
fromi day to day as tended to be the case in code 
substitution, or 
(c) Such correlations may increase from day to day. 
There is some evidence that such a tendency existed 
in the case of the abstract relations test. 


When subjects are classified upon the basis of mental age into 
superior, average, and inferior groups, the separate curves of 
such subjects may: 
(a) Converge during practice as was the case in card sort- 
ing, or 
(b) Remain roughly parallel during practice as was prac- 
tically true of the code substitution test, or 
(c) Diverge during practice as was shown by the rate 
scores of the abstract relations test. 
That the correlation between initial and final performances is 
controlled by two sorts of factors: 
(a) Specific capacities per se, which are characteristic of 
that particular mental function, and 


58 GILES MURREL RUCH 


(b) The general factor of the degree of alienation 
between the mental processes involved in the learning 
and general intelligence. Where the relation is close 
the correlations of initial and final efficiencies probably 
tend to be higher than is the case in mental function 
more distantly related to general mental capacity. 


5. That many of the disagreements among students of learning 
can be harmonized upon the hypothesis that there is no general- 
ized type of learning curve, but that learning curves are specifi- 
cally conditioned by the type of mental function and by the 
differences in the general mental capacities of the subjects. 


APPENDIX 
pepe tsi (fat: i Abneeeinatan 
Pieces at a I eed eee BED Toga ok 
LI Ae Med! i. 


AAR ee 


“|X \/ i ie ath Te 


Sgro gto op cam FA he a ea a Et 
AChE ET >) > Gy fs) Ge 
Riseca tl Gl ie ial eli ack er eee (ee 
or (oh (Rp Seal ee i ahd a 
Cala a ue aa ee Lee ees EC) Sure 
Perea Ch LG nis ern i O 
Re Nd mad Etc. 


Fig. 9—A sample of the test materials used for the code to English 
translation in the substitution experiments. The sample given covers the 
first few phrases of Chapter I of Oliver Twist. A few of the words have 
been translated in order to show the method. 


60 GILES MURREL RUCH 


A sample of the test materials! used for the English to code translation 
in the substitution experiments. The sample given covers a few phrases 
from Chapter II of Oliver Twist: 


For the next eight or 
ten months, Oliver was the 
victim of a systematic course 
of treachery and 
deception. He was 
brought up by hand. 

The hungry and destitute 
situation of the infant 
orphan was duly reported 
by the workhouse author- 
ities to the parish 
authorities. The 

parish authorities 
inquired with dignity of 
the workhouse author- 
ities, whether there 

was no female then 


1The materials as used were heavily leaded to allow the subjects to write 
the symbols between the lines. 


INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 61 


A sample of the problems used in the abstract mathematical relations 
test. The first five of the problems have already been answered in order 
to show the method by which the subjects recorded their answers to the 
problems. 


1 + Bis larger than D 

2 + Aplus D is larger than B 

3 2+ C minus D is larger than B 

4 + C minus A is less than D 

5 + A plus D is less than B plus C 

6 A minus B is less than D minus C 

7 C minus A is equal to B plus D 

8 A plus B plus D is equal to D plus C 
9 A plus B plus C is equal to B plus C plus D 
10 A minus D is larger than C minus A 
11 A is larger than C 

12 C plus D is less than B 

13 A minus C is larger than B 

14 D minus B is equal to A 

15 A plus C is larger than D minus B 

16 A minus D is less than B plus C 

17 C minus A is larger than D minus B 
18 A plus C plus D is less than D plus A 
19 A plus B plus D is equal to B plus C plus D 
20 A minus D is less than B minus D 
21 B is less than C 
22 A plus C is larger than D 

Zo A minus D is larger than C 

24 D minus C is equal to B 
25 A plus D is larger than B minus C 


Etc. 


BIBLIOGRAPHY 


1, Apetson, A. R.: The Measurement of Mental Ability of Backward 
Children, Brit. Jour. of Psych., 1911, 4, 268-314. 

2. Batpwin, B. T.: The Learning of Delinquent Adolescent Girls as 
shown by a Substitution Test, Jour. Educ. Psych., 1913, 4, 317-332. 

3. BercstroM, J. A.: An Experimental Study of Some of the Conditions 
of Mental Activity, Amer. Jour. of Psych., 1894, 6, 247-274. 

4. Binet, A.: Attention and Adaptation, L’annee Psych., 1899, 6, 248-404, 
espec., 362-381 and 402-404. 

5. Bonser, F. G.: The Reasoning Ability of Children of the Fourth, Fifth, 
and Sixth School Grades, Teach. Coll. Contr. to Educ., 1910, No. 37. 

6. Brown, WaRNER: Habit Interference in Sorting Cards, Univ. of Calif. 
Pub., 1914, 1, No. 4, 269-321. 

7. Burt, C.: Experimental Tests of General Intelligence, Brit. Jour. 
Psych., 1909, 3, 94-177. 

8. CaLFEE, M.: College Freshmen and Four General Intelligence Tests, 
Jour. Educ. Psych., 1913, 4, 223-231. 

9. CHAPMAN, C. C.: Individual Differences in Ability and Improvement 
and their Correlation, Teach. Coll. Contr. to Educ., 1914, No. 63. 

10. Corvin, S. S.: Aspects of the Learning Curve, Psych. Bull., 1915, 
ATs eg 

11. Coover, J. E., and Ancett, F.: General Practice Effects of Special 
Exercise, Amer. Jour. Psych., 1907, 328-340. 

12. Cutter, A. J.: Interference and Adaptability, Arch. of Psych., 1912, 
No. 24. 

13. DaLteNBACcH, K.: The Effect of Practice Upon Visual Apprehension 
in the Feebleminded, Jour. Educ. Psych., 1919, 10, 61-82. 

14. DEARBoRN, W. F., and Brewer, J. M.: Methods and Results of a Class 
Experiment in Learning, Jour. Educ. Psych., 1918, 9, 63-82. 

15. Donovan, M. E., and TuHornpixe, E. L.: Improvement in a Practice 
Experiment under School Conditions, Amer. Jour. Psych., 1913, 24, 426-428. 

16. Goutp, M. C., and Perrin, F. A. C.: A Comparison of the Factors 
Involved in the Maze Learning of Human Adults and Children, Jour. Exptl. 
Psych., 1916, 1, 122-154. 

17. Gray, C. T.: A Comparison of Two Types of Learning ut Means 
of a Substitution Test, Jour. Educ. Psych., 1918, 9, 143-158. 

18. Haun, H. H., and TuHornpixe, E. L.: Some’ Results of Practice in 
Addition under School Conditions, Jour. Educ. Psych., 1914, 5, 65-84. 

19. HottincwortH, H. L.: Correlations of Abilities as Affected by Prac- 
tice, Jour. Educ. Psych., 1913, 4, 405-414. 

20. Hottincwortu, H. L.: Individual Differences Before, During, and 
After Practice, Psych. Rev., 1914, 21, 1-8. 

21. Hotitincwortu, L. S.: The Psychology of Subnormal Children, 1920, 
Macmillan Co., pp. 1-228, espec., Chapter X, How Do the Mentally Defective 
Learn, 170-189. 

22. Jounson, B.: Practice Effects in a Target Test—A Comparative Study 
of Groups Varying in Intelligence, Psych. Rev., 1919, 26, 300-316. 





INFLUENCE OF INTELLIGENCE ON THE LEARNING CURVE 63 


23. Jones, E. S.: The Influence of Age and Experience on Correlations 
Concerned with Mental Tests, 1917, Warwick and York, pp. 1-89. 

24. Kirpy, T. J.: Practice in the Case of School Children, Teach. Coll. 
Contr. to Educ., 1913, No. 58. 

25. Kune, L. W., and Owens, W. A.: A Preliminary Report of a Study 
in the Learning Process Involving Feeling Tone, Transference and Inter- 
ference, Psych. Rev., 1913, 206-244. 

26. KUHLMANN, F.: Experimental Studies in Mental Deficiency, Amer. 
Jour. Psych., 1904, 15, 391-446. 

27. Loucu, J. E.: Plateaus in Simple Learning, Psych. Bull., 1912, 9, 
87-88. 

28. Murpocu, K.: Rate of Improvement of the Feebleminded as Shown 
by Standardized Educational Tests, Jour. Appl. Psych., 1918, 2, 243, 249. 

29. Munn, A. F.: The Curve of Learning, Arch. of Psych., 1909, 2, 36-52. 

30. Myers, G. C.: Some Variabilities and Correlations in Learning, Amer. 
Jour. Psych., 1918, 29, 316-326. 

31. Orpaut, L: E., and G.: Qualitative Differences Between Levels of 
Intelligence in Feebleminded Children, Jour. of Psycho-Asthenics, 1915, 
No. 2; 3-50. 

32. Perrin, F. A. C.: The Learning Curves of the Analogies and Mirror 
Reading Tests, Psych. Rev., 1915, 26, 42-62. 

33. PETERSON, J.: Tentative Norms in the Rational Learning Test, Jowr. 
App. Psych., 1920, 4, 250-257. 

34. Pye, W. H.: The Examination of School Children, 1913, pp. 1-70, 
espec., 18-22. 

35. Pyte, W. H.: Is Individual Learning Capacity Constant for Different 
Types of Material? Jour. Educ. Psych., 1919, 10, 121-128. 

36. Pyte, W. H.: The Psychology of Learning, 1920, Warwick and York, 
pp. 1- 

37. Rucer, H. A. The Psychology of Efficiency, Arch. of Psych., 1910, 
No. 15, pp. 1-88. 

38. Srmpson, B. R.: Correlations of Mental Abilities, Teach. Coll. Contr. 
to Educ., 1912, No. 53. 

39. SPEARMAN, C., and Kruecer, F.: Die Korrelation zwischen Ver- 
schiedenen Geistigen Leistungsfahigkeiten, Zeitschrift fiir Psych., 1907, 44, 
pp. 50-114. 

40. Sgutre, C. R.: Graded Mental Tests, Jour. Educ. Psych., 1912, 3, 432-4. 

41. Starcu, D.: Transfer of Training in Arithmetical Operations, Jowr. 
Educ. Psych., 1911, 2, 306-310. 

42. Starcu, D.: Periods of Work in Learning, Jour. Educ. Psych., 1912, 
3, 209-213. 

43. StRICKLAND, G. I.: The Influence of Practice on the Correlations in 
Ability, Jour. Educ. Psych., 1918, 9, 393-399. 

44. Stronc, E. K.: The Learning Curve as a Diagnostic Measure of 
General Intelligence, Psych. Bull., 1915, 12, 67-68. 

45. Terman, L. M.: Genius and Stupidity, a Study of the Intellectual 
Processes of Seven “Bright” and Seven “Stupid” Boys, Ped. Sem., 1906, 
13, 307-373. 

46. THoRNDIKE, E. L.: The Effect of Practice in the Case of a Purely 
Intellectual Function, Amer. Jour. of Psych., 1908, 19, 374-384. 


64 GILES MURREL RUCH 


47. THorNbDIKE, E. L.: Educational Psychology, Vol. III, 1914, espec., 
pp. 302-307. 

48. THorNDIKE, E. L.: Notes on Practice, Improvability, etc., Amer. Jour. 
Psych., 1915, 27, 550-553. 

49. THorNDIKE, E. L.: Practice in the Case of Addition, Amer. Jour. 
Psych., 1910, 21, 483-486. 

50. WALLIN, J. E. W.: Psychomotor Norms for Diagnosis, Psych. Rev. 
Monog. Supp., 1916, No. 94. : 

51. WEmENSALL, J.: The Mentality of the Criminal Woman, 1916, 
Warwick and York. 

52. Wetts, F. L.: Relation of Practice to Individual Differences, Amer. 
Jour. of Psych., 1912, 23, 75-88. 

53. WurpeLce, G. M.: Manual of Mental and Phyiscal Tests, 1915, 
Warwick and York, espec., pp. 133-147. 

54. Wuitety, M. T.: An Empirical Study of Several Tests for Individual 
Differences, Arch. of Psych., 1911, 19. 

55. Wooprow, H.: Practice and Transference in Normal and Feeble- 
minded Children, Jour. Educ. Psych., 1917, 8, 85-96 and 151-165. 

56. Wooprow, H.: Brightness and Dullness in Children, 1919, Lippincott. 

57. WoopwortH, R. S., and Wetts, F. L.: Association Tests, Psych. Rev. 
Monogr., 1911, No. 57, espec., 53-55. 

58. Woo.L.ey, H. T., and Fiscuer, C. R.: Mental and Physical Measure- 
ments of Working Children, Psych. Rev. Monogr., 1914, 18, No. 77, espec., 
148-184. ; 


& 


, 
pe oa 


a es 
in a . 


bi 


can ae i 





r 
yl 


» 


yt cea Tre 
AG eva y, 


if iy Vere 4 v {of 
iiead ee Py ) : 





vy th ru aah) ‘a 
aay eae! <a 
Pind iy - _, 


~ ay 


i 


man " r . 
ibe 





BF21 .P96 v.34 
The influence of tuition in the 


Princeton Theological Seminary—Speer Library 


UIE 


1 1012 00008 5474 





























iti nl ‘ t ; + 
ire { 4 Oi : . 
’ ( 
sie ’ 
\ tis Ve j 4 ae y t 
H 4a 
j t ur ' 
tome revi y { y 
, ‘ i 
; ' 
yirg : { , 
be ¢ 
; ‘ } ' 
Hib oreo ‘ ' ‘ r 
ass ' eb ryt f ; 
bid t ree 
vey { ‘ : 
VM blanca nOeGne eh nh RE SD Bed t ‘ prea 
ty poy de peley F wet ; 
bil POP UB ‘ { 
iy ory) rey? | ‘ i 
teh i i 
{ : tht 
; bei 4 it; 
' ; 
; ' 
1 iy peretsi ws f 
/ . : 
rt an ; : 
(ear hep by | r Wed 
‘ i , wine t 
He hhey il bole pier \ ; i 
by ¢ j 
' ; 
' 
whip ‘ : ‘ get ‘ ' 
ma rpiyiy) t j ees 
wily ( . 
fs 
LGNy Be VP : va 
, ’ 
f \ fet ; ¢ ye 
‘ ao 
! j : ; Hy 
t ' t is) \ l 
y 5 
t 
i 
' ( f 
Yibos ft bigs i 
i 6 : j 
‘ ‘ 
' y ty ¢ 4 
' ’ Bn cmb 
‘ f 
i ‘ , y eae ' 
' f ‘ bd ' 
we itn ; 
y) j Bb ‘ 
' the 
' ‘ 
7 ' 


